In this talk I'll present some recent results from an ongoing project with Derek Holt (Warwick) and John Bray (Queen Mary) to classify the maximal subgroups of the classical groups in dimension less than 13. The talk will focus in particular on dimension 6, as this is a good representative case. I'll show how to derive a list containing all groups that might be maximal, and then give some sketch proofs of both maximality and nonmaximality.