The two primary structures within a cell responsible for producing energy are the mitochondria and, in plant cells, chloroplasts. Mitochondria are the powerhouses of the cell, converting nutrients into ATP (adenosine triphosphate), the energy currency of the cell. Chloroplasts, found in plant cells, utilize sunlight through photosynthesis to produce glucose, which is then used by the mitochondria to generate ATP. Thus, both organelles play crucial roles in cellular energy production.