How do we learn? Donald Hebb postulated the famous Hebb's rule of learning in 1949. Tremendous progress has been made since then about the biological mechanisms of Hebbian learning, namely the NMDAR-dependent synaptic plasticity, also known as the spike timing-dependent plasticity or STDP. On the other hand, Hebbian plasticity has significant limitations in realistic, extended, noisy neurons. I will discuss computational models of the emergent properties of Hebbian learning, experimental tests of the theory on hippocampal place cells and in many other systems, and the unsolved puzzles.