The functions performed by different neural microcircuits depend on the anatomical and physiological properties of the various synaptic pathways connecting neurons. Neural microcircuits across various species and brain regions are similar in terms of their repertoire of neurotransmitters, their synaptic kinetics, their short-term and long-term plasticity, and the target-specificity of their synaptic connections. However, microcircuits can be fundamentally different in terms of the precise recurrent design used to achieve a specific functionality. In this review, which is part of the TINS Microcircuits Special Feature, we compare the connectivity designs in spinal, hippocampal, neocortical and cerebellar microcircuits, and discuss the different computational challenges that each microcircuit faces.