In most practical flow situations the boundary layer is three-dimensional rather than two-dimensional, Three-dimensional boundary-layer flows, however, are not sufficiently understood and many questions regarding their behaviour remain unanswered. In this study several different aspects of three-dimensional boundary-layer flows are investigated. Initially, through the examination of specific problems, we demonstrate the existence of discontinuous solutions in unsteady and steady three-dimensional boundary-layer flows. These case studies demonstrate the existence of pseudo-shocks and examine different aspects of discontinuous solutions, such as how they form and how the existence of a wall affects the solution. For all the problems the proper shock conditions are derived and the existence of a valid shock structure is proven. Furthermore, several new three-dimensional interactive problems with no counterpart in two-dimensional flows are investigated. These case studies illuminate how the boundary layer behaves in the presence of an obstacle for a flat plate and a curved wall configuration. For all cases the linearised problem is solved. For one of the cases a similarity solution is shown to exist and the eigensolutions which allow for upstream influence are analytically derived. For the latter case the solution of the non-linear problem is also presented. Finally, the behaviour of a steady three-dimensional boundary-layer flow, which develops under the influence of a two-dimensional vortex, is investigated numerically. This type of flows, apart from their theoretical importance in understanding three-dimensional separation, also have a significant practical relevance in aerodynamics, as they constitute an idealised model of the flow over a helicopter blade. For the particular problem it is demonstrated that, for a certain set of values of the governing parameters, the flow field develops a singularity at a finite distance from the leading edge. This singularity indicates the impossibility of unseparated flow, which the obtained numerical results suggest is a case of ordinary separation with a vortex breaking away at the position of the singularity.