Reliable path-planning and generation of collision-free trajectories has become an area of active research over the past decade where the field robotics has probably been the most active area. This paper´s main objective is to analyse the advantages and disadvantages of two of the most popular techniques used in collision-free trajectory generation in n-dimensional spaces. The importance of analysing such techniques within a generalised framework is evident as path-planning is used in a variety of fields such as designing medical drugs, computer animation and artificial intelligence and, of course, robotics. The review provided in this paper starts by drawing a historical map of path-planning and the techniques used in its early stages. The main concepts involved in artificial potential fields and probabilistic roadmaps will be addressed as these are the most influential methods and have been widely used in specialised literature.