<p>Transient absorption (TA) spectroscopy has become a widely used method for tracking photoinduced dynamics in molecules, materials, devices and biological systems. By measuring pump-induced absorption changes, TA provides direct access to excited-state populations, energy-transfer and charge-transfer processes and transient intermediates with femtosecond temporal resolution and broad spectral coverage. This Primer examines how TA spectroscopy can be used to interrogate non-equilibrium processes, introducing the physical origin of TA signals and the most common experimental implementations, with emphasis on instrumentation, measurement strategies and data analysis. We discuss practical considerations, including spectral–temporal calibration, chirp correction, global and target analysis, noise suppression and reproducibility, and highlight representative applications across chemistry, physics and materials science. Finally, we address current limitations of TA spectroscopy and outline emerging directions, including multimodal and multidimensional implementations, machine-learning-assisted analysis and integration with complementary ultrafast spectroscopies.</p>