In general, the execution of a task by a robot requires the definition of suitable motion trajectories, which may be expressed either in configuration space or in task space. The goal of trajectory planning is to generate such reference trajectories for the motion control system, which will then be in charge of tracking them as closely as possible. Many tasks are expressed in terms of an initial and a final robot state that must be connected by a continuous motion (point-to-point planning). More complex tasks may involve a sequence of intermediate points that the robot needs to go through (multi-point planning). The trajectory planning problem can be conveniently decomposed in two parts: first, defining a geometric path for the robot so as to comply with the given boundary conditions and smoothness requirements; second, choosing a timing law, which describes how the robot should trace the path over time in order to meet initial and final conditions, as well as satisfy kinetic limits. For each of these two subproblems, the chapter discusses different classes of functions (typically, piecewise polynomials of different order) that can be used to interpolate data points while taking into account additional constraints. In most cases, path planning is performed componentwise, either in configuration space or in task space depending on the specification of the problem. Nonetheless, some planning problems in task space are better addressed by directly handling vector quantities, while still separating position and orientation.