Covalent bonds result when valence electrons are shared between atoms. A covalent bond is a balance between the attractive and repulsive forces between atoms, which ends up placing electron density between the atoms. Covalent bonds are typically classified as sigma bonds (shared electrons in a cylindrically symmetrical direct line between atoms) or pi bonds (shared above and below the atoms in p orbitals), though other covalent bonds are possible. These bonds are not, however, an equal sharing of electrons between atoms, as electronegativity plays a significant factor in determining which atom has the most "desire" for the shared electrons. This results in polar covalent bonds, where one atom in a bond has a partial positive charge (like the carbon in a C-O bond) or a partial negative charge (like the oxygen in a C-O bond). These partial positive/negative charges can be significant factors in predicting how molecules react with one another. Different theoretical models of bonding have been developed to explain the behavior of molecules observed in nature: Lewis theory, valence bond theory, the hybridization model, and molecular orbital theory.
From a mathematical perspective, covalent bonds are typically formed when the electronegativity difference (Δχ) between the atoms is < 1.7 Debye