Angle-resolved photoemission spectroscopy (ARPES), with its exceptional sensitivity to both the binding energy and the momentum of valence electrons in solids, provides unparalleled insight into the electronic structure of quantum materials. Over the past two decades, the advent of femtosecond lasers, which can deliver ultrashort and coherent light pulses, has ushered the ARPES technique into the time domain. Currently time-resolved ARPES (TR-ARPES) can probe ultrafast electron dynamics and the out-of-equilibrium electronic structure, providing a wealth of information that is otherwise unattainable in conventional ARPES experiments. This review 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.

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• Electronic structure
• Phase transitions
• 2-dimensional systems
• Strongly correlated systems
• Photoelectron techniques
• Time & angle resolved photoemission spectroscopy
• Ultrafast femtosecond pump probe