Synapses of the neocortex specialized during human evolution to develop over extended timescales, process vast amounts of information and increase connectivity, which is thought to underlie our advanced social and cognitive abilities. These features reflect species-specific regulations of neuron and synapse cell biology. However, despite growing understanding of the human genome and the brain transcriptome at the single-cell level, linking human-specific genetic changes to the specialization of human synapses has remained experimentally challenging. In this review, we describe recent progress in characterizing divergent morphofunctional and developmental properties of human synapses, and we discuss new insights into the underlying molecular mechanisms. We also highlight intersections between evolutionary innovations and disorder-related dysfunctions at the synapse.