Book excerpt: All human and animal behavior from seeing, hearing, running, and falling in love, is the result of complex dynamics in a web of intricate networks in the brain. The human brain, in particular, contains close to 100 billion brain cells (or neurons) of different types connected through more than 100 trillion connections (or synapses), often in complicated patterns (or motifs) that depend on the brain area and function of the network. How these neurons and synapses are organized into specific network architectures so that neuronal activity and dynamics can give rise to behavior is still a mystery. A similar problem exists in the case of artificial neural networks: there is no systematic approach to designing artificial network architectures that generalize well across tasks, conditions, and contexts. For artificial and biological networks alike, we are interested in understanding the building blocks that permit a broad array of neural network functionality to emerge. We approach this problem from several perspectives: 1) we show how a biologically inspired microcircuit with several specific features (multiple inhibitory cell types, a comparatively smaller neuron population recurrently connected to the network that acts in a switch-like manner, and a disinhibitory network motif) is a minimally complex architecture that can switch between visual processing of the static context and the moving context; 2) we find a fast and flexible artificial network with a biologically-inspired network motif that generalizes across context when classifying visual stimuli shown sequentially and with different background contexts; 3) we begin the process of identifying new, bio-inspired network motifs via methods that identifynetwork motifs that inform neuron type classification. Our work clarifies the set of network connection structures that are both necessary and sufficient to achieve more flexible computational capability in both biological and artificial neural networks.