Garry Kimovich Kasparov the reigning Champion. After 1987 World Championship match Kasparov had time to play in tournaments again (between 1983 and 1987 he played in only 2 tournaments - winning both of them). Between 1987 and 1990 World Championship matches he played in 9 tournaments and won them all. When we add 4 consecutive tournaments that Kasparov won even before his 1st World Championship match, we get an all-time record of 15 consecutive tournament wins (shatering the previous record of 9 consecutive wins set by Karpov). Kasparov's run was finally stoped by Vasily Ivanchuk in 1991 Linares when he finished half a point ahead of Kasparov. This means that Kasparov didn't lose a single competition (either tournament or match) for a whole decade, between 1981 and 1991 !!!
In January 1990 Kasparov became the first player to surpass the 2800 rating mark. For the first time, Kasparov was seen as the clear favourite in the World championship match.
Anatoly Yevgenyevich Karpov the challenger. In 1988 Karpov tied first (with Kasparov) in the Soviet championship, won the tournaments in Wijk aan Zee, Tilburg and Brussels, finished 2nd (behind Short) in Euwe memorial, 2nd (behind Kasparov) in Belfort and Optibeurs. In 1989 he tied for first (again with Kasparov) in World Cup (Skelleftea), finished 2nd in World Cup (Rotterdam), 2nd in Linares and 3rd in Reggio Emilia. In 1990 he won the Biel tournament.
Karpov was clearly the second best player in this period.
As in all previous matches between them, it was a close match with Kasparov prevailing at the end. See here for more details about the games.
Impact on the future
Back then almost nobody imagined that this would be the last championship match between Kasparov and Karpov. In 5 close World Championship matches they played 144 games from which Kasparov won 21 games, Karpov won 19 games, and 104 games were drawn. Despite never playing in a World Championship again, the rivalry between them remained for the rest of their careers. Games between Karpov and Kasparov were always something special and gathered much attentions, no matter if they were in serious tournaments or just in promotional blitz events (even after Kasparov retired).