Peter D. Mitchell proposed the chemiosmotic hypothesis in 1961.  In brief, the hypothesis was that most adenosine triphosphate (ATP) synthesis in respiring cells comes from the electrochemical gradient across the inner membranes of mitochondria by using the energy of NADH and FADH formed during the oxidative breakdown of energy-rich molecules such as glucose.
Molecules such as glucose are metabolized to produce acetyl CoA as a fairly energy-rich intermediate. The oxidation of acetyl coenzyme A (acetyl-CoA) in the mitochondrial matrix is coupled to the reduction of a carrier molecule such as nicotinamide adenine dinucleotide (NAD) and flavin adenine dinucleotide (FAD).
The carriers pass electrons to the electron transport chain (ETC) in the inner mitochondrial membrane, which in turn pass them to other proteins in the ETC. The energy at every redox transfer step is used to pump protons from the matrix into the intermembrane space, storing energy in the form of a transmembrane electrochemical gradient. The protons move back across the inner membrane through the enzyme ATP synthase. The flow of protons back into the matrix of the mitochondrion via ATP synthase provides enough energy for ADP to combine with inorganic phosphate to form ATP.
This was a radical proposal at the time, and was not well accepted. The prevailing view was that the energy of electron transfer was stored as a stable high potential intermediate, a chemically more conservative concept. The problem with the older paradigm is that no high energy intermediate was ever found, and the evidence for proton pumping by the complexes of the electron transfer chain grew too great to be ignored. Eventually the weight of evidence began to favor the chemiosmotic hypothesis, and in 1978 Peter D. Mitchell was awarded the Nobel Prize in Chemistry.
Chemiosmotic coupling is important for ATP production in mitochondria, chloroplasts
and many bacteria and archaea.