Angle-resolved photoemission spectroscopy (ARPES) — an experimental technique based on the photoelectric effect — is arguably the most powerful method for probing the electronic structure of solids. The past decade has witnessed notable progress in ARPES, including the rapid development of soft-X-ray ARPES, time-resolved ARPES, spin-resolved ARPES and spatially resolved ARPES, as well as considerable improvements in energy and momentum resolution. Consequently, ARPES has emerged as an indispensable experimental probe in the study of topological materials, which have characteristic non-trivial bulk and surface electronic structures that can be directly detected by ARPES. Over the past few years, ARPES has had a crucial role in several landmark discoveries in topological materials, including the identification of topological insulators and topological Dirac and Weyl semimetals. In this Technical Review, we assess the latest developments in different ARPES techniques and illustrate the capabilities of these techniques with applications in the study of topological materials.