Brain synapses are neuronal structures of the greatest interest. For a long time, however, the knowledge about them was variable, and interest was mostly focused on their pre-synaptic portions, especially neurotransmitter release from axon terminals. In the present review interest is focused on post-synapses, the structures receiving and converting pre-synaptic messages. Upon further modulation, such messages are transferred to dendritic fibers. Dendrites are profoundly different from axons; they are shorter and of variable thickness. Their post-synapses are of two types. Those called flat/intended/aspines, integrated into dendritic fibers, are very frequent in inhibitory neurons. The spines, small and stemming protrusions, connected to dendritic fibers by their necks, are present in almost all excitatory neurons. Several structures and functions including the post-synaptic densities and associated proteins, the nanoscale mechanisms of compartmentalization, the cytoskeletons of actin and microtubules, are analogous in the two post-synaptic forms. However other properties, such as plasticity and its functions of learning and memory, are largely distinct. Several properties of spines, including emersion from dendritic fibers, growth, change in shape and decreases in size up to disappearance, are specific. Spinal heads correspond to largely independent signaling compartments. They are motile, their local signaling is fast, however transport through their thin necks is slow. When single spines are activated separately, their dendritic effects are often lacking; when multiple spines are activated concomitantly, their effects take place. Defects of post-synaptic responses, especially those of spines, take place in various brain diseases. Here alterations affecting symptoms and future therapy are shown to occur in neurodegenerative diseases and autism spectrum disorders.