In their temperature window of application, TiAl alloys typically fail in a semi-brittle manner. For this material class, the Griffith concept, developed initially for ideal brittle materials, has to be adapted by additional dissipative contributions to the fracture resistance: plastic deformation, crack bridging, the work to deform and fracture shear ledges, and crack bifurcation. These additional terms in the fracture resistance induce a pronounced R-curve effect or in other words, a crack extension-dependent fracture resistance for monotonic and cyclic loading. In order to deliver guidelines to optimize the microstructural design and to enhance the fracture resistance of TiAl alloys, model systems, including a polysynthetically twinned TiAl, a designed fully lamellar and a near-gamma TiAl alloy are discussed in terms of their fracture mechanism using the energy and stress intensity approach.