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Angle-resolved photoemission spectroscopy (ARPES) -- with its exceptionalsensitivity to both the binding energy and momentum of valence electrons insolids -- provides unparalleled insights into the electronic structure ofquantum materials. Over the last two decades, the advent of femtosecond lasers,which can deliver ultrashort and coherent light pulses, has ushered the ARPEStechnique into the time domain. Now, time-resolved ARPES (TR-ARPES) can probeultrafast electron dynamics and the out-of-equilibrium electronic structure,providing a wealth of information otherwise unattainable in conventional ARPESexperiments. This paper begins with an introduction to the theoreticalunderpinnings of TR-ARPES followed by a description of recent advances instate-of-the-art ultrafast sources and optical excitation schemes. It thenreviews paradigmatic phenomena investigated by TR-ARPES thus far, such asout-of-equilibrium electronic states and their spin dynamics, Floquet-Volkovstates, photoinduced phase transitions, electron-phonon coupling, and surfacephotovoltage effects. Each section highlights TR-ARPES data from diverseclasses of quantum materials, including semiconductors, charge-ordered systems,topological materials, excitonic insulators, van der Waals materials, andunconventional superconductors. These examples demonstrate how TR-ARPES hasplayed a critical role in unraveling the complex dynamical properties ofquantum materials. The conclusion outlines possible future directions andopportunities for this powerful technique.

Time- and Angle-Resolved Photoemission Studies of Quantum Materials