1. Glycolysis: This is the first stage, occurring in the cytoplasm of the cell. It breaks down glucose (a 6-carbon sugar) into two molecules of pyruvate (a 3-carbon molecule). This process produces a small amount of ATP (energy currency) and NADH (electron carrier).

2. Krebs Cycle (also called the Citric Acid Cycle) and Oxidative Phosphorylation: These processes occur in the mitochondria.

* Krebs Cycle: The pyruvate produced from glycolysis is further broken down, releasing carbon dioxide and generating more NADH and FADH2 (another electron carrier).

* Oxidative Phosphorylation: The NADH and FADH2 deliver electrons to the electron transport chain, which ultimately results in the production of a large amount of ATP through a process called chemiosmosis. This process also requires oxygen.

Key takeaway: While glycolysis happens outside the mitochondria, the Krebs Cycle and oxidative phosphorylation happen inside the mitochondria, which is the "powerhouse" of the cell.