1. Mitochondria: This is the primary site of ATP production in eukaryotic cells. The process is called oxidative phosphorylation, and it involves a series of reactions within the mitochondrial matrix and the inner mitochondrial membrane. This is where the energy from the breakdown of glucose and other fuels is used to generate ATP.

2. Cytoplasm: A smaller amount of ATP can be produced in the cytoplasm through a process called glycolysis, which is the breakdown of glucose into pyruvate. This process does not require oxygen and can occur even in the absence of mitochondria.

Therefore, while the majority of ATP is produced in the mitochondria, a small amount is also produced in the cytoplasm.