Twisted magnetic flux ropes are ubiquitous in laboratory and astrophysical plasmas, and the merging of such flux ropes through magnetic reconnection is an important mechanism for restructuring magnetic fields and releasing free magnetic energy. The merging-compression scenario is one possible start-up scheme for spherical tokamaks, which has been used on the Mega Amp Spherical Tokamak (MAST). Two current-carrying plasma rings or flux ropes approach each due to mutual attraction, forming a current sheet and subsequently merge through magnetic reconnection into a single plasma torus, with substantial plasma heating. Two-dimensional resistive and Hall-magnetohydrodynamic simulations of this process are reported, including a strong guide field. A model of the merging based on helicity-conserving relaxation to a minimum energy state is also presented, extending previous work to tight-aspect-ratio toroidal geometry. This model leads to a prediction of the final state of the merging, in good agreement with simulations and experiment, as well as the average temperature rise. A relaxation model of reconnection between two or more flux ropes in the solar corona is also described, allowing for different senses of twist, and the implications for heating of the solar corona are discussed.