Since the discovery of superhumps in 1974, these photometric modulations have provided a crucial observational window into disk instabilities in cataclysmic variable stars, particularly the tidal instability associated with the 3:1 resonance. Over the past few decades, extensive time-resolved photometry has revealed a rich diversity of superhump-related phenomena, including delayed superhump development, early superhumps in WZ Sge-type dwarf novae, systematic stage A-B-C evolution, negative superhumps, and superhumps observed in related systems, intermediate polars, AM CVn stars and black hole X-ray binaries.
In this review, we summarize key observational advances since the establishment of the thermal-tidal instability framework, discuss their theoretical interpretations within the disk instability model, and highlight remaining open problems. These developments have been driven by coordinated networks of amateur observers, wide-field robotic surveys, and continuous high-precision space-based photometry from Kepler and TESS. Together, they demonstrate that superhumps remain a powerful probe of disk dynamics, binary parameters, and the interplay between thermal, tidal, and geometric effects in accretion disks.