In this paper a combination of experimentation and analysis is used to identify and study the mechanisms that govern the failure of unidirectional fiber composites under compression. The experimental part includes experiments in which the compressive strength and the prevalent failure mechanisms of AS4/PEEK composite are established, tests for establishing the constitutive properties of the composite and its constituents, and an evaluation of the extent of misalignment of fibers in manufactured composites. The failure load of the composite was confirmed to be affected by geometric imperfections in the form of fiber waviness, and failure was found to lead to kink bands with distinct orientations and widths. Motivated by the experimental findings, the composite was idealized as a two-dimensional solid with alternating fiber and matrix layers, each having the measured properties of the two constituents. The compressive responses of microsections of finite width with imperfections of various spatial distributions were established numerically. The calculated responses are characterized by an initially stiff, stable regime terminated by a limit load instability which is associated with the strength of the composite. Following the limit load, the deformation localized into inclined bands with distinct widths. It has been verified that, as the localization process progresses, the fiber bending stresses at the ends of these bands grow to values comparable to those of the fiber strength. The sensitivity of the calculated response to the geometric characteristics of the imperfections was studied parametrically.