Spiking neural P systems (SN P systems) are a mathematical model of neural networks, abstracting the way biological neurons communicate with spikes, developed within the framework of the membrane computing theory. Recently, driven by the boom of learning neural models, SN P systems have become a rapidly emerging research front. Consequently, many different variants of the learning models of SN P system prevail among the new research results. Although large proprietary deep learning models are still based on the continuous neural network paradigm, spiking neurons are attractive because of their low-energy demands. The purpose of this paper is to provide an up-to-date overview of learning paradigms and techniques for SN P systems. After a brief introduction of the structure and function of SN P systems, we summarise recent approaches to learning and adaptation in SN P systems, including Hebbian learning, Widrow-Hoff algorithm, fuzzy approaches, nonlinear SN P systems, gated and long short-term memory inspired SN P systems, convolutional SN P systems, and more.