Methods of modifying sawtooth oscillations using waves in the ion cyclotron range of frequencies (ICRF) in the JET tokamak are presented. Examples of sawtooth stabilization by ICRF-accelerated high-energy ions are shown, including experiments with ICRF-acceleration of 4He-beam ions to simulate the effects of fusion born alpha particles. With high power ICRF heating in low-density plasmas, fast ion stabilization of sawteeth is lost and a new type of small-period and small-amplitude sawteeth appears. ICRF-induced radial pinch with toroidally asymmetric waves is found to be useful in affecting the radial profile of the ICRF-driven fast ion populations and thereby their influence on sawteeth. Ion cyclotron current drive (ICCD) applied close to the sawtooth inversion radius is effective in modifying the sawtooth period. The latest achievements include the successful application of ICCD to shorten the fast-ioninduced long-period sawteeth and thereby avoid triggering of neoclassical tearing modes (NTMs).