Propulsive effects of light, which often remain unnoticed in our daily-life experience, manifest themselves on spatial scales ranging from subatomic to astronomical. Light-mediated forces can indeed confine individual atoms, cooling their effective temperature very close to absolute zero, as well as contribute to cosmological phenomena such as the formation of stellar planetary systems. In this review, we focus on the transport processes that light can initiate on small spatial scales. In particular, we discuss in depth various light-induced mechanisms for the controlled transport of microscopic particles; these mechanisms rely on the direct transfer of momentum between the particles and the incident light waves, on the combination of optical forces with external forces of other nature, and on light-triggered phoretic motion. After a concise theoretical overview of the physical origins of optical forces, we describe how these forces can be harnessed to guide particles either in continuous bulk media or in the proximity of a constraining interface under various configurations of the illuminating light beams (radiative, evanescent, or plasmonics fields). Subsequently, we introduce particle transport techniques that complement optical forces with counteracting forces of non-optical nature. We finally discuss particle actuation schemes where light acts as a fine knob to trigger and/or modulate phoretic motion in spatial gradients of non-optical (e.g., electric, chemical, or temperature) fields. We conclude by outlining possible future fundamental and applied directions for research in light-induced particle transport. We believe that this comprehensive review can inspire diverse, interdisciplinary scientific communities to devise novel, unorthodox ways of assembling and manipulating materials with light.