This study presents measurements of sheet flow processes, grain sorting, and bedload plus suspended load transport rates around a medium-sand breaker bar in a large-scale wave flume. The results offer insights in effects of wave breaking on bedload and grain sorting processes and in the quantitative contributions by bedload and suspended transport to breaker bar morphodynamics. Sheet flow layer dynamics are highly similar to observations under non-breaking waves, revealing clear effects by velocity asymmetry but no evident effects by breaking-generated turbulence, bed slope, or the cross-shore non-uniform flow. The sheet flow layer thickness can be predicted using existing empirical formulations based on local hydrodynamic forcing. At locations covering the shoaling region up to the bar crest the cross-shore variation in bedload transport rates is explained by variations in wave shape (i.e. velocity skewness and asymmetry). At locations between bar crest and bar trough, bedload transport rate magnitudes correlate positively with bed slope and turbulent kinetic energy. Bedload and suspended load transport rates are of similar magnitude but of opposite sign. Bedload transport is onshore-directed and dominates in the shoaling zone, but after wave breaking, the offshore-directed suspended sediment transport increases in magnitude and exceeds bedload transport rates in the breaking and inner surf zones. Bedload and suspended load transport contribute notably differently to bed profile evolution: bedload transfers sand grains from the offshore slope to the bar crest and additionally leads to erosion of the shoreward bar slope and deposition at the bar trough, while suspended load transport induces an opposite pattern of erosion at the bar trough and accretion at the bar crest. Grain size analysis of suspended sediment samples reveals size-selective entrainment and vertical size segregation in the inner surf zone, but suggest size-indifferent entrainment and vertical mixing by energetic vortices in the breaking region. Size-selective transport by bedload and suspended load leads to a cross-shore coarsening of the bed from shoaling to inner surf zone, with local additional sorting mechanisms around the breaker bar due to bed slope effects.