Abstract Waves are an important agent in the construction, shaping and destruction of river deltas. Notwithstanding the commonality of waves in oceans and seas, wave influence on deltas varies considerably depending on the coastal morphology and nearshore bathymetry. Although there have been advances in understanding the way waves approaching a delta shape its shoreline, much still remains to be known of the interactions between waves and river deltas. Deltas are built essentially from sediments supplied by rivers. Sand-sized and coarser sediments may also be derived from nearby abandoned delta lobes or from older relict nearshore deposits, transported by wave reworking and longshore currents. Alternatively, delta erosion by waves can also release sediment that is redistributed alongshore or that accumulates offshore. The extent to which bedload is supplied to and sequestered in, or lost by, deltas through waves and longshore transport strongly depends on interactions between waves and fluvial discharge at the river mouth. These interactions and the mutual adjustments they engender are not only important in the overall balance between delta retreat, progradation or aggradation but also in processes such as avulsion and channel switching, as well as in the eventual survival of a delta in the face of sea-level rise. Where waves are important, fluvial liquid discharge is high, and sediment supply is rich in bedload, two important aspects are the blocking of waves and longshore currents by strong river discharge and the formation of bars at the river mouth. Field studies of the complex interactive processes prevailing where river flows encounter waves are, however, non-existent and numerical modelling, though promising, hampered by scale constraints and the difficulty of replicating them and generating mouth bars in the presence of longshore currents. This interaction influences the seaward extent of the delta mouth protuberance and its stability; this protuberance then forming the regional shoreline template to which waves and longshore currents adjust. Longshore currents can redistribute wave-reworked mouth bar deposits emplaced during strong river flow. Transport may be either divergent from the mouth or may be regionally unidirectional but wherein the symmetry of some deltas, probably rare, may be maintained by a strong river blocking effect on transport from the updrift flank. The mouth protuberance may be such as to foster transport reversal (counter-drift) at the delta margins that contributes to sediment sequestering within the delta. These interactions largely contribute in shaping delta shorelines, and together with the abundance of sediment supply and grain size, determine the resultant wave-formed shoreline barrier types, which include spits, more or less closely-spaced beach ridges, and barrier islands and cheniers in situations of punctuated progradation or retreat. Where several distributary mouths occur, pronounced longshore variability in wave processes and wave-induced sediment transport may ensue, resulting in multiple drift cells that assure the retention of sand and coarse-grained sediments within the delta. Waves can also be an important agent in the reworking and retreat of mud-rich deltas that generally conform in morphology to the ‘river-dominated’ (such as the Mississippi) or ‘tide-dominated’ (such as the Ganges–Brahmaputra or Chao Phraya) types, resulting in the episodic formation of sandy cheniers and beach ridges. Although sea-level rise is likely to lead to enhanced wave reworking of deltas, the possible prevalence of aggradation (in lieu of progradation), channel switching and avulsion, and washover processes, may contribute to the disorganization of waves and longshore transport, fostering deltaic sequestering of sand and coarser-sized sediment and delta survival. The weakening of river discharges resulting from human activities will invariably lead, however, to enhanced wave reworking of deltas and to deltaic sediment redistribution by longshore currents. The massive swing towards significant reductions in fluvial sediment supply today may signify the ultimate demise of many deltas in the coming decades through a process of delta shoreline straightening by waves, in addition to accelerated sinking. These various foregoing aspects of the relationship between waves and river deltas are reviewed here across a range of timescales, and new interaction concepts proposed, using numerous examples of deltas in the world and on the basis of case studies, conceptual studies and numerical modelling studies in the literature spanning more than forty years.