Collisionless reconnection - considered to be a fundamental process in Astrophysics - can now be observed in laboratory plasmas close to thermonuclear breakeven conditions. In particular, because of the high temperatures which have been attained in recent experiments, this process is now thought to occur during the so-called "sawtooth" relaxation oscillations which affect the interior of a magnetically confined, current-carrying plasma. We review novel linear and nonlinear theoretical efforts applied to the understanding of sawtooth oscillations in regimes where the relaxation rate is determined by the plasma skin depth and by the ion Larmor radius, rather than by Coulomb collisions.