Hebbian synaptic plasticity is currently the main framework to relate neuronal activity, network structure, and learning and memory. However, recent experimental and computational modeling studies have revealed a new form of synaptic plasticity termed behavioral timescale synaptic plasticity (BTSP). It is triggered by dendritic plateau potentials associated with somatic burst firing, causes large changes in synaptic strength in a single shot, and operates on the timescale of seconds. Here we review the recent advances in our understanding of the circuit, cellular, and molecular mechanisms of BTSP, its prevalence in the brain, its role in shaping neuronal representations, and the emerging ideas regarding its contribution to different forms of learning.