Indications for Surgical Intervention
Distal talofibular ligament sprain with widened ankle mortise
It is generally accepted that for most patients, operative repair of third-degree anterior talofibular ligament (ATFL) tears and medial ankle ligament tears does not contribute to an improved outcome. 
One of the few absolute indications for surgery in patients with a sprained ankle is a distal talofibular ligament third-degree sprain that causes widening of the ankle mortise. To restore the ankle mortise, the distal tibiofibular articulation must be screwed together.
The usual postoperative course entails avoiding weight-bearing for 6 weeks, followed by removal of the screw and then continuing external immobilization while allowing weight-bearing for an additional 6 weeks. This program serves to avoid breakage of the syndesmotic screw and the associated difficulties that may present.
Deltoid sprain with widening of medial ankle mortise
A second indication for surgical treatment of acute ankle sprains is a deltoid sprain with the deltoid ligament caught intra-articularly and with widening of the medial ankle mortise.
Isolated lateral ligament sprains
In 100 patients with isolated lateral ligament sprains, Evans et al found no functional or symptomatic advantage 2 years after injury in patients who were treated surgically as compared with those who were treated with cast immobilization.  In fact, the nonsurgically treated group returned to work earlier and had less morbidity than the surgically treated patients. Patients in this study were divided into two groups, each with 30 individuals with anterior ligament sprains only and 20 individuals with anterior and middle ligament ruptures. One group of 50 patients was treated surgically, and the other group was treated with cast immobilization.
Double lateral ligament tears
Staples reported that young, active, athletic patients with tears of both the ATFL and the calcaneofibular ligament (CFL) are best treated surgically. His cohorts included a group of young athletic patients with only 58% satisfactory results after immobilization and a subsequent, similar group of patients who had 88.9% satisfactory results with surgical repair. In the group of patients who underwent surgery, the average hospital stay was 7.6 days, and six (22.2%) of 27 patients had complications. Marginal necrosis of the skin at the wound edge and hypesthesia of the fourth and fifth toes and adjacent forepart of the foot were the only reported complications. 
Entrapped deltoid ligament
An isolated complete medial ankle sprain with a palpable defect and demonstrable clinical instability is an indication for surgery, particularly if the deltoid ligament is caught in the medial ankle joint. Surgery allows removal of the ligament from the joint and repair of the ligament.
Go to Ankle Sprain for more complete information on this topic.
Surgery for Chronic Ankle Instability
Selection of operative approach
According to a review by Safran et al, more than 20 different delayed surgical procedures are available for chronic ankle instability and sprains.  Most of these procedures are reconstructive in nature, and many involve tenodesis between the lateral malleolus and calcaneus, talar head, and/or the fifth metatarsal. All of these procedures use the peroneus brevis and/or longus, Achilles tendon, or fascia lata. None of them really restores the true ankle anatomy.
The surgical treatment decision for chronic medial instability involves determining whether the tissues are of good or bad quality. If the tissues are of good quality, a direct reattachment can be performed. If the tissues are of poor quality, a free flexor digitorum longus graft can be used that goes from the tibia into the talus or navicular to reconstruct the deltoid ligament.
For syndesmotic sprains, surgical treatment depends on whether any arthritic change is present. If the articular surface is destroyed on both sides of the joint, tibiotalar arthrodesis or arthroplasty is necessary. In patients with diastasis without significant tibiotalar arthritis, late reduction of the syndesmosis and reconstruction of the ligaments are recommended. 
Broström described a repair that reapproximates the ruptured ligaments and restores true normal anatomy of the ankle. Some clinicians have declared this procedure to be hazardous, in that finding healthy margins of the ruptured ligament tissue is difficult.
Gould et al described a modified Broström procedure that allowed reinforcement of the repair and limited inversion (reducing the likelihood of injury) and that helped to correct the subtalar component to the instability.  This modified procedure permitted restoration of the normal anatomy and preserved normal ankle motion with less surgical exposure. The incision is performed from an anterolateral approach, paralleling the fibula border, and starting from the level of the plafond distally to the level of the peroneal tendons. Dissection is then carried down to the capsule. If no obvious anterior talofibular ligament (ATFL) rupture is present, the capsule and ligaments are divided for a few millimeters and then imbricated. [6, 7, 8]
The peroneal sheath is then opened to determine the quality of the calcaneofibular ligament (CFL) . If the CFL is stretched, it can be divided and imbricated.  If this ligament is ruptured, a distal avulsion from the calcaneus can be reattached with a suture anchor. A proximal avulsion can be reattached with sutures through drill holes in the fibula. 
For midsubstance tears, determine whether the remnant can be imbricated. If it cannot, some surgeons have used the posterior talofibular ligament (PTFL) by releasing it from its talar insertion and swinging it distally to insert at the calcaneal insertion site of the CFL. The most important thing to consider here is that there is no anterior displacement force on the ankle while the sutures are being tied. A bump is usually placed under the calf. Stability is checked before closure. Further stability (and possibly proprioception) is provided to the subtalar area by imbrication of the inferior extensor retinaculum (IER) to the periosteum over the fibula.
Once the skin is closed (usually with subcuticular stitching), a U-shaped splint and a posterior splint or walking boot are applied.
An arthroscopic variant of the Broström procedure has been described. 
Other surgical options, as mentioned above, are mainly tenodesis procedures, of which the following four have been extensively used and described in the literature:
These procedures focus on harvesting all or part of the peroneus brevis and then rerouting the tendon through various bone tunnels, thereby creating a tenodesis of the ankle or reconstructing the ATFL or the CFL. Indications for these augmented types of reconstruction are as follows:
The ATFL and CFL are so disrupted and frayed that they cannot be repaired primarily
Hypermobility of the subtalar joint is present
The patient has had previously unsuccessful reconstruction of the ankle
For each of these procedures, the overall technical approach is essentially the same. A longitudinal incision is made running just posterior to the prominence of the lateral malleolus. The incision is then extended to allow harvesting of the peroneus brevis tendon. Before harvesting the tendon, the joint is inspected and debrided if necessary. Occasionally, the ATFL, the CFL, or both are avulsed from the fibula with a piece of bone. This so-called os subfibulare should be excised.
Maintain the integrity of the superior peroneal retinaculum upon exposure of the peroneus brevis tendon. The anterior one third of the tendon is isolated distally and split from the distal position to the musculoskeletal junction. This tendon portion is transected at its proximal aspect. A drill hole is made through the distal fibula, and the split portion of the peroneus brevis is passed through this hole. The tendon is tensioned with the foot in mild plantarflexion and eversion.
The Evans procedure provides stability that is a result of the ATFL and CFL but not anatomically or mechanically. The peroneus brevis tendon is anchored to the fibula, indirectly limiting inversion of the ankle and anterior talar translation, while also limiting motion of the subtalar joint.
The Watson-Jones procedure reconstructs the ATFL but not the CFL. This technique makes use of the Evans tenodesis. One important addition, however, is that the peroneus brevis graft is routed anteriorly through the talar neck to reconstruct the ATFL.
Larsen rerouted the peroneus brevis tendon from the fifth metatarsal base into the fibula and then back down into the calcaneus. The proximal part of the tendon is sutured to the peroneus longus. 
The Chrisman-Snook procedure, most commonly used for subtalar instability, involves using half of the longitudinally divided peroneus brevis tendon to substitute or reconstruct the CFL. In this procedure, the peroneus brevis graft is brought through the fibula from anterior to posterior to reconstruct the ATFL. It is then brought posteriorly and inferiorly to the calcaneus in a weave pattern to reconstruct the CFL. The Chrisman-Snook procedure, though technically demanding, has been repeatedly demonstrated to produce satisfactory stability to those patients who have a talotibial and combined talotibial and talocalcaneal instability.
Triligamentous reconstruction uses half of the peroneus brevis tendon to substitute for the ATFL, the CFL, and the cervical ligament (CL). This procedure efficiently addresses talotibial and talocalcaneal instability. Despite its success, triligamentous reconstruction is a technically demanding procedure.
Outcomes of operative repair
These procedures vary greatly with regard to their ability to correct subtalar instability. In the literature, the Watson-Jones procedure is associated with subjective instability 20-90% of the time; the Evans procedure, 20-33%. In addition, with the Evans procedure, a persistent anterior drawer sign is found in 45-60% of patients. In the Chrisman-Snook procedure, 13-30% of patients had subjective persistent instability. Decreased inversion is common with all these procedures. In each procedure, a specific weave pattern (referring to the manner in which the peroneus brevis tendon is routed through the drill holes) is used.
In a study by Kim et al, chronic syndesmotic instability and chronic medial ankle instability were found to be significantly associated with unsatisfactory outcomes in patients with chronic ankle instability who had undergone treatment with a modified Broström procedure. 
The cause of continued symptoms after ankle sprain, regardless of the method of treatment, is incompletely understood. Equal supervision of the postinjury course may tend to lessen the difference in outcomes between the surgical and conservative treatment protocols.
Newer methods of bracing, such as a controlled ankle motion (CAM) walker and air cast-type braces, protect well while allowing mobility and may provide better outcomes than does rigid casting. Further research is needed to determine the best treatment for complete double-ligament lateral ankle sprains.