The talk will review the development in the field of DNA-related topological problems, knots and links formed by double-stranded DNA molecules. It will start from purely theoretical problem of calculating the equilibrium probability of knots in a polymer chain. Although solving this problem was an achievement in polymer statistical physics, it did not look useful for anything else at that time. Eventually, however, it helped greatly in the studies of DNA general properties and its topological transformations catalyzed by site-specific recombinases and DNA topoisomerases. Some examples of these applications will be briefly considered. The second half of the talk will be concentrated on an amazing property of type II DNA topoisomerases, the ability of these enzymes to reduce fractions of knots and links in circular DNA molecules below the level that corresponds to the thermodynamic equilibrium.