Magnetic reconnection is a fundamental process in a plasma that facilitates the release of energy stored in the magnetic field by permitting a change in the magnetic topology. In this paper, we present a review of the current state of understanding of magnetic reconnection. We discuss theoretical results regarding the formation of current sheets in complex three-dimensional magnetic fields and describe the fundamental differences between reconnection in two and three dimensions. We go on to outline recent developments in modelling of reconnection with kinetic theory, as well as in the magnetohydrodynamic framework where a number of new three-dimensional reconnection regimes have been identified. We discuss evidence from observations and simulations of Solar System plasmas that support this theory and summarize some prominent locations in which this new reconnection theory is relevant in astrophysical plasmas.