Dirac and Weyl semimetals react to position- and time-dependent perturbations, such as strain or an inhomogeneous magnetisation, as if emergent electromagnetic fields were applied. Such pseudo-electromagnetic fields differ from external electromagnetic fields in their symmetries and phenomenology, and enable a simple and unified description of a variety of inhomogeneous systems. We review the different mechanisms for creating effective pseudo-fields and their observable consequences, which can be remarkably different from those resulting from external fields