We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we propose an efficient feed forward architecture derived from the iteration of the block-coordinate algorithm. This architecture approximates the exact structured sparse codes with a fraction of the complexity of the standard optimization methods. We also show that by using different training objective functions, the proposed learnable sparse encoders are not only restricted to be approximants of the exact sparse code for a pre-given dictionary, but can be rather used as full-featured sparse encoders or even modelers. A simple implementation shows several orders of magnitude speedup compared to the state-of-the-art exact optimization algorithms at minimal performance degradation, making the proposed framework suitable for real time and large-scale applications. Copyright 2012 by the author(s)/owner(s).