  Dirac and Weyl semimetals, materials where electrons behave as relativistic
fermions, react to position- and time-dependent perturbations, such as strain,
as if emergent electromagnetic fields were applied. Since they differ from
external electromagnetic fields in their symmetries and phenomenology they are
called pseudo-electromagnetic fields, and enable a simple and unified
description of a variety of inhomogeneous systems involving topological
semimetals. We review the different physical ways to create effective
pseudo-fields, their observable consequences as well as their similarities and
differences compared to electromagnetic fields. Among these difference is their
effect on quantum anomalies, the absence of a classical symmetry in the quantum
theory, which we revisit from a quantum field theory and a semiclassical
viewpoint. We conclude with predicted observable signatures of the
pseudo-fields and the nascent experimental status.

Mesoscale and Nanoscale Physics;Materials Science