Are you a fan of such cop shows as “The Wire” or “C.S.I.”? If so, you owe a little debt of gratitude to “Miami Vice.”

I hear you scoffing. None of the police officers on your favorite show run around in Italian suits (over T-shirts!) and pastel colors or own a pet alligator named Elvis. But … hit songs that play while the crime goes down? Conflicted cops who can be as dirty as the bad guys? Crooks who sometimes get away with it? Multiracial casts with a variety of ethnicities on both sides of the law? Trace them all back to “Vice.”

All were signatures of the style-over-substance series that ran from 1984 to 1989 and chronicled the adventures of Sonny Crockett (Don Johnson) and Rico Tubbs (Philip Michael Thomas). You can see for yourself with the release of “Miami Vice: The Complete Series” ($199.98, but it can be found for $50 less) on Tuesday.

Brandon Tartikoff, then with NBC, is credited with inspiring the show’s essence with the phrase “MTV cops.” Full of color and flash, most of the stories had plot holes and unbelievable aspects. (For one thing, why are “undercover” cops Crockett and Tubbs hanging out at the police station so much?) But that didn’t matter because the show looked great and sounded better, surpassing anything else on TV at the time in both regards.

The sound is the most compelling aspect of this release. It has all the original songs in Dolby Digital 5.1 surround sound. The show featured music from Phil Collins, U2, Peter Gabriel, Glenn Frey, Guns N’ Roses, The Cure, Public Enemy and other big names. Once it became hip, musicians wanted to have their songs included. Securing the rights to the wide assortment of songs was one reason it took so many years before the series began making its way to DVD.

Packaged in a fake alligator skin box, this set includes all five seasons. Bonus features include “The Vibe of Vice,” which explores how the show changed the television landscape; “Building the Perfect Vice,” which traces the show from its development to airing; “The Style of Vice,” a look at how the show took European fashion trends and made them popular across America; “The Music of Vice,” a look at the integral role music played in the series’ storytelling; and “Miami After Vice,” a look at the city where the show was set. Most of these are interesting, although you would expect more extras for a complete-series box.

The show itself so perfectly captured the ’80s zeitgeist that it does feel a bit dated. That’s partly because of its success: So many aspects, techniques and themes from the show have become commonplace that it almost feels cliched because you forget you’re watching the innovator.

If you’re a fan who hasn’t bought all the seasons individually, the set is a nice purchase. But if you have each release, you can safely skip this collection.