In this paper, recent theoretical developments on Anderson localization in one-dimensional electron systems are reviewed. First, the theories for noninteracting systems are summarized together with the various results based on numerical simulation. Special attention will be paid to the dynamical structure of the systems. The second part discussed Anderson localization in interacting electron systems by the phase Hamiltonian, and the close relationship between the localization and the impurity pinning of charge density wave is demonstrated. Results of the numerical simulations by quantum Monte Carlo technique are also presented.