The Pursuit Special (or the V8 "Interceptor" as it is more commonly known) is the iconic, jet black, muscle car driven by "Mad" Max Rockatansky. The vehicle itself, despite being the most iconic item from the franchise, only appears in three of the Mad Max films (these being Mad Max, Mad Max 2: The Road Warrior and, most recently, Mad Max: Fury Road. The car was absent in the third film after the events that occurred in The Road Warrior) as well as the Mad Max video game released in 2015 and furthermore, is only fully featured in the first film with the later films only briefly showing the vehicle or, in the case of Mad Max 3: Beyond Thunderdome, not featured or mentioned at all. The V8 in it's name refers to the engine it uses which is obviously a more powerful upgrade from the V6 engine, the car has a reputation in the films for being incredibly fast (with nearly unrivaled acceleration and maximum speed) and how it is surprisingly resilient and hardy for a vehicle which is classified as a 'coupe' series vehicle.
Mad Max 
In the original 1979 cult-classic film, the Pursuit Special (the main Pursuit Special as there is a second briefly featured in the opening sequence to the film) is a modified version of a 1973 Ford Falcon XB GT model, which is offered to lead protagonist of the series, Max Rockatansky (played by Mel Gibson) in an attempt made by the police department to persuade him to remain on the police force after Max openly raised his intention to resign from the force. Additionally, it seems as though Max was also offered the vehicle as he would be the only driver skilled enough to control it, being the top pursuit man on the police force. Goose even directly references this fact when first revealing the vehicle to Max. Although Max declines, remarking that giving him the car would not make him reconsider quitting, Max later returns to the police station and claims the vehicle as his own in order to extract revenge on the gang that murdered his wife and child as well severely burning his best friend, Goose, leaving him in critical condition in the hospital (where he presumably succumbed to his injuries)
Mad Max 2 (The Road Warrior) 
In the second film, Mad Max 2 (The Road Warrior) released two years after the original, the trademark car makes it return, still being commandeered by Max. However, it seems that between the events of the first and second film, the car had received a number of modifications, both within the filming process and the canon of the Mad Max story (The original car used had to be reacquired by the film crew as it was sold shortly after the completion of the first film) these new modifications included numerous body parts being replaced (including replacing the rear wheels, side-pipes as well as the fitting of a functional Supercharger as opposed to the broken one used in first film) a total cosmetic overhaul; giving the car an overall more weathered and scarred appearance (the jet black paintwork was removed to give the car a suitably 'rusted' look for the new desert wasteland setting) and an armed, explosive device was wired to the bottom of the vehicle by Max to be used as a last resort should his life be put in severe danger. During the events of the second film, the Interceptor is completely destroyed after Max detonates the bomb strapped to the car after he is run off the road by the main antagonists of the film, which promptly leaves him without a vehicle (and explains why the vehicle was absent in the third film).
Mad Max: Fury Road 
Despite the car being absent throughout the entirety of the third film, the famous vehicle made a return in the fourth and most recent film, Fury Road, however it only appeared briefly as it is destroyed once again during the climax of the film. The vehicle's appearance in this film also marks the first time where the car is not solely driven by Max, as it (alongside Max, now played by Tom Hardy) is captured during the opening events of the film, where the car is shown being repaired heavily modified by a group of Immortan Joe followers when Max attempts to make his escape. It is later seen again being driven by one of the War Boys in the final battle, only to be crushed between two large vehicles where it promptly explodes.
The fate of the vehicle is unconfirmed (as of 2016), it is assumed that the collision would have almost completely destroyed the car which would make it near impossible to have the car be repaired and even more so, in fully-functioning condition. Many assume that this may be the last appearance of the Interceptor however, besides the first two films, the Mad Max series doesn't have a official timeline of events, combined with the popularity of the vehicle among both die-hard fans and casual movie goers, it is likely that the Interceptor will be featured again in some form or another. The fact that Max has shown to be a skilled mechanic in previous films, it isn't completely impossible that Max could repair the Interceptor by salvaging parts from other vehicles however this depends entirely on the fate of the car (mainly the chassis).
Mad Max (the 2015 video game)
In the 2015 video game, Max is ambushed by a group of War Boys led by Scabrous Scrotus (Son of Immortan Joe and Warlord of the area south of Gastown - which are both referenced to directly in Mad Max Fury Road) which leads to the vehicle being stolen from Max and seemingly scrapped by Scrotus' war boys. Max, with the aid of Chumbucket (a skilled black-finger - or car mechanic - who regards the Magnum Opus as a sort of religious symbol, referring to Max as the 'Saint') spends the majority of the game building a replacement vehicle known as the 'Magnum Opus' (which the player modifies and upgrades over the course of the game) with which he can use to take revenge on Scrotus and his War Boys. In the final confrontation, despite pleas by Chumbucket, the Opus (which is now a worthy rival to the V8 Interceptor - complete with a high powered harpoon and an engine to rival the black-on-black) is destroyed in an attempt to finish off Scrotus (but ultimately fails). However, after the final battle between Max and Scrotus, the War Lord is killed and Max manages to re-obtain his Interceptor (albeit in a more damaged state) and drives it off into the wastelands alone once more.