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Abstract: Nuclear fusion of light elements is the mechanism that powers stars and could become a source of energy on Earth. This talk reviews main approaches and achievements obtained in magnetic confinement fusion machines called tokamaks and stellarators. By considering the ignition criterion applied to magnetic fusion, three main strategic avenues are identified for the developments of magnetic fusion machines: i) large volume machines with long plasma confinement time, ii) machines with high magnetic field, and iii) compact size spherical tokamaks with high values of plasma pressure. Present-day experiments on tokamaks JET, C-MOD, and MAST representing the three avenues above are compared and the next-step burning plasma ITER project is discussed. In preparation for the burning plasma experiment with significant plasma self-heating by fusion-born alpha-particles (He ions with birth energy 3.5 MeV), studies on alpha-particle confinement and Alfvénic instabilities driven by these alpha-particles are currently one of the main topics in magnetic fusion. Numerous observations of discrete Alfvén eigenmodes driven by energetic ions in present-day machines are presented. Main theoretical approaches for investigating Alfvén instabilities are described for both linear threshold estimates and for nonlinear evolution of the instabilities.