The magnetotransport properties of three new superconducting compounds (Y l-xCaxBa2Cu307-8, ThBa2Cu06+8 and RNhB2C) have been investigated. The study has principally involved measurements of the anisotropic resistivity, magnetoresistance, and Hall effect of these compounds, using a new 15 Tesla superconducting magnet system. Results of measurements of the resistivity, Hall effect and magnetoresistance of sintered and thin film samples of Y l-xCaxBa2Cu307-8 are presented. The Hall coefficient of the fully oxygenated overdoped material is smaller in magnitude and has a weaker temperature dependence than that of optimally doped material, while the resistivity has an upward curvature and can be well fitted by A + BT + CT2. Despite these large changes in P and RH, cot(SH) shows remarkably little variation with doping, as is the case for underdoped YBa2Cu307-8. In addition, it is shown that overdoping Y l-xCaxBa2Cu307-8 causes the mixed-state resistivity to shift rather than broaden in applied magnetic fields. Measurements of the c-axis magnetoresistance of single crystals of T12Ba2Cu06+8 (TI-2201) reveal a striking four-fold angular dependence as the magnetic field is rotated in the ab-plane. A metallic c-axis resistivity (dpc/dT > 0) indicates that the out-of-plane transport may be coherent, and based on this assumption a simple model for this system is developed, using Boltzmann transport theory with an anisotropic relaxation time 'to CalCulations based on this model are used to extract the anisotropy in the in-plane mean free path from the experimental results. It is shown the measured changes in the anisotropy in 't cannot fully account for the temperature dependence of the in-plane Hall coefficient. Furthermore, despite a metallic c-axis resistivity, the c-axis mean free path is estimated to be less than the c-axis lattice parameter for all but the lowest temperatures. Finally, the new class of rare earth intermetallic borocarbides RNi2B2C has been investigated. The results of resistivity, susceptibility, thermoelectric power, Hall effect and magnetoresistance measurements are presented for nonsuperconducting and superconducting, magnetic and nonmagnetic members of this family (R = Y, La, Ho, Er, Lu). These results clarify the nature of the electronic transport in these compounds, and reveal some important connections between the normal-state properties and the superconductivity. In particular, measurements of single-crystals show for the first time that Pc = Pa. Furthermore, a negative longitudinal magnetoresistance in HoNhB2C above TN, which scales as HIT, demonstrates unambiguously the presence of spin-disorder scattering in this compound.