A review of the present theoretical understanding of the linear stability of internal m=1 modes is presented and its connection to phenomena observed in toroidal magnetic confinement experiments, i.e. 'sawtooth' and 'fishbone' oscillations, is discussed. Particular attention is devoted to the analysis of non-magnetohydrodynamic (non-MHD) effects, such as those due to finite diamagnetic and electron drift frequencies and to finite ion Larmor radius, and to the special role played by energetic particles (whose response is primarily kinetic and which can stabilize low frequency modes and destabilize new, higher frequency, branches). Some recent developments in the non-linear theory of these modes are also discussed. This review complements that of Kuvshinov and Savrukhin (Sov. J. Plasma Phys. 16 (1990) 353)