Various compounds (Tl-2223, Tl-1223, TI-2212) as well as material forms (single crystals, thin films, ceramics, tapes) of TI-based high temperature superconductors were investigated by magnetic and transport techniques. The Tl-2223 material has a very low lying irreversibility line (H||c) and negligible critical current densities J_c at 77 K. However, the irreversibility line is shifted to higher fields and temperatures, and J_c is strongly enhanced even at 77 K, after fast neutron irradiation. In contrast, the related Tl-1223 compound has a much steeper irreversibility line (H||c) similar to the one of Y-123. J_c is significant up to 77 K, even in the unirradiated state. Transport measurements made on Tl-1223 tapes still show much lower critical current densities. Tl-2212 and Tl-2223 thin films have J_c values at 77 K, which are comparable to those of the Tl-1223 single crystal.