In markets for beef and sheep meat, an appropriate level of intramuscular fat (IMF) is highly desirable for meat-eating quality, but strategies to improve it usually lead to an undesirable excess in carcase fat, presenting a major challenge to livestock producers. To solve this problem, we need to understand the partitioning of fat among the major fat depots: IMF, subcutaneous fat (SCF) and visceral fat (VF). In most genotypes of cattle and sheep, the rate of accretion is lower for IMF than for SCF and VF, so genetic selection for a high level of IMF, or the use of an increased dietary energy supply to promote IMF deposition, will increase overall fatness and feed costs. On the other hand, feeding postnatal calves with excessive concentrates promotes IMF deposition, so a nutritional strategy is feasible. With genetic strategies, several problems arise: 1) positive genetic correlations between IMF, SCF and VF differ among genotypes in both cattle and sheep; 2) genotypes appear to have specific, characteristic rates of accretion of IMF during periods of growth and fattening; 3) most breeds of cattle and sheep naturally produce meat with relatively low levels of IMF, but IMF does vary substantially among individuals and breeds so progress is possible through accurate measurement of IMF. Therefore, an essential prerequisite for selection will be knowledge of the genetic correlations and fat accretion rates for each genotype. Currently, selection for IMF is based on existing technology that directly measures IMF in the progeny or siblings, or estimates IMF in live animals. New technology is needed to permit the simultaneous measurement of SCF and IMF in the field, thus opening up the possibility of accurate selection, particularly for fat partitioning in live animals. Specifically, there would be great value in detecting individuals with an IMF advantage at an early age so the generation interval could be shortened and genetic gain accelerated. Genetic gain would also be greatly aided if we could select for genes that control adipogenesis and lipogenesis and are also differentially expressed in the various depots.