When atoms are brought together, their atomic orbitals may approach each other in close enough proximity to interact. In the formation of covalent bonds, the electrons in the atomic orbitals (s and p sublevel primarily) of one atom interact with the electrons in the atomic orbitals of another atom to accomplish the sharing of electrons between the atoms.
The interaction between atomic orbitals involves primarily, but not entirely, an interaction of one orbital of one atom with an orbital of another atom.
There are two common bond categories, sigma bonds and pi bonds. Both types are created by the interaction of specific atomic orbitals in well defined orientations.
A problem with just considering atomic orbital overlap is that geometries are not well predicted. In the valence bond theory, first developed by Linus Pauling, atomic orbitals first interact to form hybrid orbitals, and these hybrids overlap with either other hybrids or other unhybridized atomic orbitals to form bonds.
