Rice productivity in irrigated ecosystems is strongly governed by the balance between source capacity, sink strength, and the efficiency of assimilate transport. Despite high input availability, yield gains often remain inconsistent due to physiological constraints operating at different developmental stages. This review synthesises current knowledge on source–sink relationships in irrigated rice, with emphasis on photosynthetic capacity, carbohydrate partitioning, phloem transport, grain filling dynamics, and their regulation by agronomic and genetic factors. Evidence from physiological, biochemical, and molecular studies is integrated to explain how source activity, sink size, and transport processes interact to determine final grain yield. Important challenges include stage-specific limitations in assimilate translocation and sink unloading under high resource inputs, along with frequent mismatches between enhanced sink potential and transport or remobilisation capacity. By integrating physiological, biochemical, and molecular insights, this review (i) identifies stage-specific source or sink limitations in irrigated rice systems and (ii) proposes an integrated framework for breeding and management strategies that align source longevity with efficient sink unloading. The insights presented provide a basis for developing yield-stable rice ideotypes and optimising management practices in intensive irrigated environments.