Much of respiration takes place in the mitochondria.
Mitochondria have a double membrane: the outer membrane contains
many protein channels, which let almost any small molecule through;
while the inner membrane is more normal and is impermeable to most
materials. The inner membrane is highly folded into folds called
cristae, giving a larger surface area. The electron microscope
reveals blobs on the inner membrane, which were originally called
stalked particles. These have now been identified as the enzyme
complex that synthesises ATP, are is more correctly called ATP
synthase. the space inside the inner membrane is called the matrix,
and is where the Krebs cycle takes place (the matrix also contains
DNA and some genes are replicated and expressed here).