High accuracy quantum mechanical studies of functions of enzymes is a relatively new branch of biochemistry, now about a decade old. The method of preference has been density functional theory (DFT) in its hybrid form, where a fraction of exact exchange is introduced. In the present talk I will describe results obtained in the area of bioenergetics, which by tradition includes photosynthesis and respiration. The reactions involved in these two cases are their opposites, formation of oxygen from water and burning of oxygen to water, respectively. The general strategy to attack the complex enzyme systems involved will be described. The emphasis will be on the combination of insight and technical advancements necessary to reach interesting conclusions, which is particularly well illustrated by the studies on respiration. In photosynthesis a break-through for this approach was made recently. A few years ago a prediction of both mechanism of oxygen formation and structure of the manganese catalyst was made based on DFT model studies. The first high-resolution X-ray structure has just appeared (Shen et al, Nature, in press), showing that the structure of the catalyst is nearly identical to the one predicted by theory.