The uniformity of the cortical architecture and the ability of functions to move to different areas of cortex following early damage strongly suggest that there is a single basic learning algorithm for extracting underlying structure from richly structured, high-dimensional sensory data. There have been many attempts to design such an algorithm, but until recently they all suffered from serious computational weaknesses. This chapter describes several of the proposed algorithms and shows how they can be combined to produce hybrid methods that work efficiently in networks with many layers and millions of adaptive connections.