  Angle-resolved photoemission spectroscopy (ARPES) -- with its exceptional
sensitivity to both the binding energy and momentum of valence electrons in
solids -- provides unparalleled insights into the electronic structure of
quantum materials. Over the last two decades, the advent of femtosecond lasers,
which can deliver ultrashort and coherent light pulses, has ushered the ARPES
technique into the time domain. Now, time-resolved ARPES (TR-ARPES) can probe
ultrafast electron dynamics and the out-of-equilibrium electronic structure,
providing a wealth of information otherwise unattainable in conventional ARPES
experiments. This paper begins with an introduction to the theoretical
underpinnings of TR-ARPES followed by a description of recent advances in
state-of-the-art ultrafast sources and optical excitation schemes. It then
reviews paradigmatic phenomena investigated by TR-ARPES thus far, such as
out-of-equilibrium electronic states and their spin dynamics, Floquet-Volkov
states, photoinduced phase transitions, electron-phonon coupling, and surface
photovoltage effects. Each section highlights TR-ARPES data from diverse
classes of quantum materials, including semiconductors, charge-ordered systems,
topological materials, excitonic insulators, van der Waals materials, and
unconventional superconductors. These examples demonstrate how TR-ARPES has
played a critical role in unraveling the complex dynamical properties of
quantum materials. The conclusion outlines possible future directions and
opportunities for this powerful technique.
