Irradiation effects on Tl- and Y-based high temperature superconductors (HTS) are compared. Ion irradiation can enhance the critical current density (J(c)) at low fluences through the interaction of defects with the flux lattice, and at higher fluences ion irradiation can degrade the superconducting transition temperature (T(c)) and increase the normal state resistivity (rho). Low-influence irradiation of Tl2Ca2Ba2Cu3O10 (Tl-2223) single crystals was shown to increase J(c) by an order of magnitude over J(c) for unirradiated crystals. Similarly, irradiated YBa2Cu3O7-delta (YBCO) crystals have increased J(c)s by factors of 2 to 100; however, the effects of irradiation on thin-film HTS from these two materials depends greatly on their crystalline quality. Ion irradiation of millimeter grain-size Tl-2223 films was shown to increase J(c) while similar irradiation of approximately 10-mu-m grain-size Tl-2223 films had little effect on J(c). For ions with energies less than several MeV/amu, the dominant mechanism causing irradiation-induced degradation of T(c) is collisional damage. Both Tl-based and YBCO superconductors behave similarly in that T(c) decreases linearly with the level of damage; yet, the rate of decrease in T(c) for Tl-based superconductors (5000 K/dpa) was approximately twice that for irradiated YBCO. An examination of the temperature behavior and rate of damage recovery of rho yielded an activation energy of 0.36 eV for annealing defects.