This document will review the most prominent proposals using multilayer convolutional architectures. Importantly, the various components of a typical convolutional network will be discussed through a review of different approaches that base their design decisions on biological findings and/or sound theoretical bases. In addition, the different attempts at understanding ConvNets via visualizations and empirical studies will be reviewed. The ultimate goal is to shed light on the role of each layer of processing involved in a ConvNet architecture, distill what we currently understand about ConvNets and highlight critical open problems. What Do We Understand About Convolutional Networks