Among the crystalline rare earth laser hosts the isotropic sesquioxides Sc2O3, Y2O3, and Lu2O3 (cubic bixbyite structure) are known for their superior thermo-mechanical properties. Their thermal conductivity considerably exceeds that of Y3Al5O12 (YAG). Their low phonon energy ensures large energy storage times by minimizing non-radiative relaxation processes. Yb-doped sesquioxides exhibit somewhat broader absorption and emission bandwidths than Yb:YAG which is advantageous for uncritical diode laser pumping and short pulse generation. The splitting of the lower Yb3+ manifold is also larger which is important in the quasi-four-level operation scheme. Solid solutions with the isostructural Yb2O3 are possible but the observed strong lifetime quenching makes the sesquioxide hosts more suitable for laser geometries that profit from relatively low Yb concentrations. Lu2O3 is the host whose thermal conductivity is least affected by Yb-doping. The high melting point (above 2400°C) makes it difficult to grow the sesquioxides from the melt. Recently, the use of the heat-exchanger-method (HEM) allowed to considerably enhance the optical quality of the grown crystals and the available single crystal size. Here we review the properties and present laser results obtained recently with Yb-doped sesquioxide crystals in the continuous-wave (cw) and mode-locked (picosecond and femtosecond) regimes using both Ti:sapphire and diode-laser pumping. In the cw regime optical-to-optical efficiency of 62.2% and slope efficiency of 72.7% were reached with Yb:Sc2O3 operating at 1041.6 nm. Passive mode-locking of both Yb:Sc2O3 and Yb:Lu2O3 was achieved by semiconductor saturable absorber mirrors. Pulse durations of the order of 200 fs were obtained with intracavity dispersion compensation.