Understanding how individual neurons integrate the thousands of synaptic inputs they receive is critical to understanding how the brain works. Modeling studies in silico and experimental work in vitro, dating back more than half a century, have revealed that neurons can perform a variety of different passive and active forms of synaptic integration on their inputs. But how are synaptic inputs integrated in the intact brain? With the development of new techniques, this question has recently received substantial attention, with new findings suggesting that many of the forms of synaptic integration observed in vitro also occur in vivo, including in awake animals. Here we review six decades of progress, which collectively highlights the complex ways that single neurons integrate their inputs, emphasizing the critical role of dendrites in information processing in the brain.