Because of the low mobility of phosphate in soil, the acquisition of phosphorus (P) from infertile soil is dependent on the spatial exploration of the soil by plant roots and their symbionts. Soil exploration by plant roots is a function of root growth and architecture. Several root architectural traits under genetic control in crop plants are important for P acquisition, including basal root gravitropism, basal root whorl number, adventitious rooting, root hair length and density, and lateral branching. The metabolic cost of root growth and soil exploration is an important limitation to plant growth in infertile soil, and several traits under genetic control influence root cost, most notably root etiolation and root cortical aerenchyma. Root exudates that solubilize P in the rhizosphere, including phosphatases and organic anions, are also under genetic control. Phosphorus availability in the rhizosphere is also influenced by rhizosphere micro-organisms, and the P nutrition of most crops is benefited by symbiotic association with arbuscular mycorrhizas. There is genetic variation for ability to exploit the mycorrhizal symbiosis, but functional compensation of mycorrhizal and host plant traits makes the adaptive value of this variation uncertain. Biological nitrogen fixation (BNF) by legumes in symbiosis with Rhizobium bacteria is a P-intensive process and is often limited by P availability in infertile soils. Crop genotypes with superior ability to acquire P from infertile soil and superior ability to utilize P inputs can be generated by selection for these root traits. Some of these traits may have agroecological tradeoffs in specific environments that need to be better understood before germplasm deployment.