According to Arrhenius's original molecular definition, an acid is a substance that dissociates in aqueous solution, releasing the hydrogen ion  (a proton):
The equilibrium constant for this dissociation reaction is known as a dissociation constant. The liberated proton combines with a water molecule to give a hydronium (or oxonium) ion  (naked protons do not exist in solution), and so Arrhenius later proposed that the dissociation should be written as an acid–base reaction:
Brønsted and Lowry generalised this further to a proton exchange reaction:
The acid loses a proton, leaving a conjugate base; the proton is transferred to the base, creating a conjugate acid. For aqueous solutions of an acid HA, the base is water; the conjugate base is  and the conjugate acid is the hydronium ion. The Brønsted–Lowry definition applies to other solvents, such as dimethyl sulfoxide: the solvent S acts as a base, accepting a proton and forming the conjugate acid .
In solution chemistry, it is common to use  as an abbreviation for the solvated hydrogen ion, regardless of the solvent. In aqueous solution  denotes a solvated hydronium ion rather than a proton.
The designation of an acid or base as "conjugate" depends on the context. The conjugate acid  of a base B dissociates according to
which is the reverse of the equilibrium
The hydroxide ion , a well known base, is here acting as the conjugate base of the acid water. Acids and bases are thus regarded simply as donors and acceptors of protons respectively.
A broader definition of acid dissociation includes hydrolysis, in which protons are produced by the splitting of water molecules. For example, boric acid () produces  as if it were a proton donor, but it has been confirmed by Raman spectroscopy that this is due to the hydrolysis equilibrium:
Similarly, metal ion hydrolysis causes ions such as  to behave as weak acids:
According to Lewis's original definition, an acid is a substance that accepts an electron pair to form a coordinate covalent bond.