Mitochondria are double membrane-bound organelles present in almost all eukaryotic cells, responsible for producing the majority of cellular ATP through oxidative phosphorylation. They range from 1-10 micrometres in length and are often described as the "powerhouse of the cell." The number of mitochondria per cell varies widely: red blood cells have none; liver cells (hepatocytes) contain approximately 1,000-2,000; cardiac muscle cells and other highly active cells may contain thousands. Mitochondria can also fuse and divide (mitochondrial dynamics — fusion and fission), forming dynamic networks within cells rather than existing as discrete, static organelles. According to the endosymbiotic theory, mitochondria evolved from ancient alpha-proteobacteria that were engulfed by a primitive eukaryotic ancestor approximately 1.5-2 billion years ago, explaining their bacterial-like double membrane, circular DNA, and 70S ribosomes.

Outer mitochondrial membrane: smooth, relatively permeable (contains large pore-forming proteins called porins or VDACs — voltage-dependent anion channels) that allow passage of molecules up to ~5 kDa, including ATP, ADP, pyruvate, fatty acids, and various metabolites. Intermembrane space: between outer and inner membranes; similar ionic composition to cytosol but contains specific proteins including cytochrome c (important electron carrier and apoptosis signal), adenylate kinase, creatine kinase, and other enzymes. Inner mitochondrial membrane: extensively folded into cristae; completely impermeable to H+ and most ions and metabolites (transport requires specific carrier proteins); contains the respiratory chain complexes (I-IV), ATP synthase (Complex V), and numerous transport proteins. Matrix: enclosed by inner membrane; viscous gel containing all Krebs cycle enzymes, fatty acid beta-oxidation enzymes, pyruvate dehydrogenase complex, mitochondrial DNA, 70S ribosomes, and high concentrations of metabolic intermediates.

The mitochondrial matrix is where the core metabolic oxidation reactions of cellular respiration take place. Krebs cycle (TCA cycle / citric acid cycle): a cyclic series of 8 enzymatic reactions in which acetyl-CoA (derived from pyruvate, fatty acids, or amino acids) is completely oxidised to CO2, with the concurrent reduction of NAD+ to NADH and FAD to FADH2 (the exception: succinate dehydrogenase, which catalyses step 6 of the Krebs cycle, is embedded in the inner membrane as part of Complex II). Pyruvate oxidation: pyruvate dehydrogenase complex converts pyruvate (from glycolysis in cytoplasm) to acetyl-CoA + CO2 + NADH. Fatty acid beta-oxidation: sequential removal of 2-carbon acetyl units from fatty acids, each cycle producing NADH, FADH2, and acetyl-CoA. Amino acid catabolism: various transamination and deamination reactions. The NADH and FADH2 produced in the matrix carry high-energy electrons to the inner membrane electron transport chain for ATP synthesis.

ATP synthesis by the mitochondrial ATP synthase (Complex V, also called F1F0-ATPase) follows the chemiosmotic theory proposed by Peter Mitchell (1961, Nobel Prize 1978). Electron transport chain (Complexes I-IV) in the inner mitochondrial membrane oxidises NADH and FADH2, transferring electrons ultimately to O2 (forming water) and using the released energy to pump H+ from the matrix to the intermembrane space. This creates an electrochemical proton gradient (proton motive force, PMF) across the inner membrane — high H+ concentration in the intermembrane space, low in matrix. H+ ions flow back down their electrochemical gradient through the ATP synthase channel (F0 subunit embedded in inner membrane), driving rotation of the F0 rotor. This mechanical rotation drives conformational changes in the F1 catalytic subunit in the matrix, causing synthesis of ATP from ADP + Pi. Approximately 2.5 ATP are synthesised per NADH oxidised and approximately 1.5 ATP per FADH2 oxidised, giving a total of approximately 30-32 ATP per glucose molecule through complete aerobic respiration.