Dietary triacylglycerols (TAGs) are the major lipid components in the human diet and they are carriers of energy as well as important fatty acids. Many factors affect the digestion and absorption of TAGs. Evidence is accumulating that, in addition to the overall fatty acid profile, the TAG structure and the species composition are of importance when considering the nutritional effects of a dietary fat. There is good evidence that in addition to its short-term effects in the intestine on absorption of fatty acids the TAG structure also has long-term effects resulting from differences in the profile of absorbed fatty acids. Observations on the different atherogenic potential of dietary fats have given us a clear indication of the importance of the TAG structure for absorption of saturated fatty acids. In this context, one may focus on the effects of the structure of dietary fats as such, or one may speculate additionally on the possibilities of modifying the structure of fats to affect their absorption and the distribution of the fatty acids in the body after digestion and uptake. In this review we will summarize diverse aspects of TAG digestion and absorption, as well as the influences of the fatty acid composition and the intramolecular structure of dietary TAGs on their digestion and absorption.