A coalgebra \(C\) is said to be right serial if its right injective indecomposable comodules are uniserial and \(C\) is said to be serial if it is right and left serial. Several equivalent characterizations of serial coalgebras are given, for instance any finite dimensional right comodule is a direct sum of homogeneous uniserial comodules. The main result establishes that over an algebraically closed field \(k\) the basic coalgebra of a serial indecomposable coalgebra is a subcoalgebra of a path coalgebra \(k\Gamma\) where the quiver \(\Gamma\) is either a cycle or a chain (either finite or infinite). If \(C\) is cocommutative then \(C\) is isomorphic to a direct sum of subcoalgebras of the divided power coalgebra.