We present a new class of density estimation models, Structural Maxent models, with feature functions selected from a union of possibly very complex sub-families and yet benefiting from strong learning guarantees. The design of our models is based on a new principle supported by uniform convergence bounds and taking into consideration the complexity of the different sub-families composing the full set of features. We prove new data-dependent learning bounds for our models, expressed in terms of the Rademacher complexities of these sub-families. We also prove a duality theorem, which we use to derive our Structural Maxent algorithm. We give a full description of our algorithm, including the details of its derivation, and report the results of several experiments demonstrating that its performance improves on that of existing L1-norm regularized Maxent algorithms. We further similarly define conditional Structural Maxent models for multi-class classification problems. These are conditional probability models also making use of a union of possibly complex feature subfamilies. We prove a duality theorem for these models as well, which reveals their connection with existing binary and multi-class deep boosting algorithms.