valence bond theory
Picture each atom holding out a partly filled hand of electrons, and a bond forming when two atoms clasp a matching hand each. Valence bond theory keeps electrons attached to their own atoms and makes a bond wherever two half-filled atomic orbitals overlap and pair up their electrons. It is the quantum-mechanical backbone of the familiar 'shared pair' picture.
Precisely, valence bond theory describes a covalent bond as the overlap of two atomic orbitals, each contributing one electron, which then pair with opposite spins in the region of overlap. The more the orbitals overlap, the stronger the bond. To explain real molecular shapes, the theory mixes an atom's orbitals into new hybrid orbitals that point in the right directions — this is the source of ideas like sp³ hybridization.
Valence bond theory is intuitive and maps cleanly onto Lewis structures and bond diagrams, which is why it dominates introductory chemistry. Its honest limitation is that, by keeping electrons localized between specific atom pairs, it handles spread-out (delocalized) electrons awkwardly and needs the extra device of resonance; for those situations molecular orbital theory is often cleaner.
Valence bond theory explains methane (CH₄) by mixing carbon's one 2s and three 2p orbitals into four identical sp³ hybrid orbitals. Each hybrid overlaps with a hydrogen's 1s orbital, giving four equal bonds pointing to the corners of a tetrahedron — matching the measured shape exactly.
Hybridization lets valence bond theory reproduce real molecular shapes.
Valence bond theory and molecular orbital theory are not rivals about what is 'true' — they are two approximations of the same quantum reality. VB is more intuitive and local; MO is better for delocalized electrons, magnetism, and spectra. Chemists pick whichever makes a given problem easier.