Neuromorphic engineering (NE) is an emerging research field that has been attempting to identify neural types of computational principles, by implementing biophysically realistic models of neural systems in Very Large Scale Integration (VLSI) technology. Remarkable progress has been made recently, and complex artificial neural sensory-motor systems can be built using this technology. Today, however, NE stands before a large conceptual challenge that must be met before there will be significant progress toward an age of genuinely intelligent neuromorphic machines. The challenge is to bridge the gap from reactive systems to ones that are cognitive in quality. In this paper, we describe recent advancements in NE, and present examples of neuromorphic circuits that can be used as tools to address this challenge. Specifically, we show how VLSI networks of spiking neurons with spike-based plasticity mechanisms and soft winner-take-all architectures represent important building blocks useful for implementing artificial neural systems able to exhibit basic cognitive abilities.