Synaptic plasticity is considered to be the basis of learning and memory in the brain. It supports a broad range of behaviors, from the acquisition of low level task-specific skills to the emergence of high level cognitive capabilities. Understanding the computational foundations of synaptic plasticity is therefore a growing research that inspires progress in the design of autonomous adaptive systems. In that perspective, a large number of brain-inspired learning rules have been modeled and implemented. Locality, a fundamental computational principle of biological synaptic plasticity, is a key requirement for physical implementation of learning rules. In this talk we provide an overview of models and circuits for spike-based local synaptic plasticity. This overview provides the background for presenting our recent work aimed at the implementation neuromorphic hardware for learning systems.