The degree by which a species can adapt to the demands of its changing environment defines how well it can exploit the resources of new ecological niches. Since the nervous system is the seat of an organism's behavior, studying adaptation starts from there. The nervous system adapts through neuronal plasticity, which may be considered as the brain's reaction to environmental perturbations. In a natural setting, these perturbations are always changing. As such, a full understanding of how the brain functions requires studying neuronal plasticity under temporally varying stimulation conditions, i.e., studying the role of plasticity in carrying out spatiotemporal computations. It is only then that we can fully benefit from the full potential of neural information processing to build powerful brain-inspired adaptive technologies. Here, we focus on homeostatic plasticity, where certain properties of the neural machinery are regulated so that they remain within a functionally and metabolically desirable range. Our main goal is to illustrate how homeostatic plasticity interacting with associative mechanisms is functionally relevant for spatiotemporal computations. The thesis consists of three studies that share two features: (1) homeostatic and synaptic plasticity act on a dynamical system such as a recurrent neural network. (2) The dynamical system is nonautonomous, that is, it is subject to temporally varying stimulation. In the first study, we develop a rigorous theory of spatiotemporal representations and computations, and the role of plasticity. Within the developed theory, we show that homeostatic plasticity increases the capacity of the network to encode spatiotemporal patterns, and that synaptic plasticity associates these patterns to network states. The second study applies the insights from the first study to the single node delay-coupled reservoir computing architecture, or DCR. The DCR's activity is sampled at several computational units. We derive a homeostatic plasticity rule acting on these units. We analytically show that the rule balances between the two necessary processes for spatiotemporal computations identified in the first study. As a result, we show that the computational power of the DCR significantly increases. The third study considers minimal neural control of robots. We show that recurrent neural control with homeostatic synaptic dynamics endows the robots with memory. We show through demonstrations that this memory is necessary for generating behaviors like obstacle-avoidance of a wheel-driven robot and stable hexapod locomotion.