The "base" of their defense is Saban's cover 7, which has been in use by him since his Michigan State days, but obviously adjustments have been made over time by both him and Smart to combat the modern shift to spread offenses that's occurred over the past 10-15 years. Here's a video from Smart himself on the(what he calls) mint front changes, and the 2nd video is a instructional video from former Alabama DB coach Karl Scott that gets in to some of the more modern applications of Cover 7 overall, and the 3rd video is from Saban's time at MSU explaining cover 7.
Here's an excellent article from Football Advantage that goes over the basics as well:
https://footballadvantage.com/cover-7/