Synapses are the hallmark of brain complexity and have long been thought of as simple connectors between neurons. We are now in an era in which we know the full complement of synapse proteins and this has created an existential crisis because the molecular complexity far exceeds the requirements of most simple models of synaptic function. Studies of the organisation of proteome complexity and its evolution provide surprising new insights that challenge existing dogma and promote the development of new theories about the origins and role of synapses in behaviour. The postsynaptic proteome of excitatory synapses is a structure with high molecular complexity and sophisticated computational properties that is disrupted in over 130 brain diseases. A key goal of 21st-century neuroscience is to develop comprehensive molecular datasets on the brain and develop theories that explain the molecular basis of behaviour.