Generator-coordinate methods make use of variational parameters in microsopic or many-body wave functions to describe collective degrees of freedom. The use of these methods in symmetry restoration, nuclear rotational and vibrational states is described. Numerical applications in various nuclear structure problems are briefly reviewed. The structure of the integral wave equation appearing in the method is briefly discussed. Applications of these methods to study nuclear reactions are reported. These methods permit microscopic descriptions of collective nuclear properties, especially in low-energy situations requiring the use of antisymmetrized wave functions.