Recent advances in deep learning enable artificial neural networks to perform a number of specialized tasks, albeit using learning rules which are not biologically realistic. At the same time, in neuroscience, while reasonable models of biological neural activation, synaptic transmission and synaptic plasticity have been developed, it has still proven difficult to deploy these in networks that learn cognitive function. An ongoing effort in the computational neuroscience community is to construct neural network models that are simultaneously biologically realistic and functionally sophisticated. I will present some of my work that tries to solve parts of this puzzle. In particular, I will introduce a biologically-plausible plasticity rule derived from adaptive control theory that enables stable learning of body dynamics for movement control. I will also briefly highlight work on learning simple cognitive tasks in a biologically-plausible manner. I will try to keep the talk accessible to the broad IST audience.