classical modular curves associated to gl(2) are moduli spaces of elliptic curves with additional structure. taking advantage of the analogy between number fields and function fields, drinfeld modules (of rank 2) were introduced as a good analogue of elliptic curves. while there are no shimura varieties associated to the general linear group gl(n) for n$>$2, the situation is sharply different over function fields. the drinfeld modular variety for gl(n) is a moduli space of drinfeld modules of rank n (with auxiliary level structure). it is an affine scheme of dimension n-1. in this talk, i will explain how analogues of well-established theories due to hida and coleman in the classical p-adic context extend to drinfeld modular varieties and their associated modular forms. joint with g. rosso (montr\'eal).