The story of Aleste concerns the manmade supercomputer DIA 51, which has been infected by a hybrid virus that is spreading like wildfire, eventually leading DIA 51 to eliminate the human race. When Yuri, Ray's girlfriend, gets injured in DIA's assault, Raymond Waizen has all the reason in the world to get rid of DIA 51 once and for all in his Aleste fighter.
Aleste is more or less the sequel to Zanac, as it features the same AI generated enemy waves and weapon system. It did, however, start a whole new plot - evil plant creatures were taking over the planet, so you fight against monstrous vines and other types of twisted vegetation. The scrolling is also much improved over the choppiness of the original Zanac MSX.