In this thesis, the superconducting properties of some unconventional superconductors have been investigated using low temperature magnetic, thermal and transport measurements, small angle neutron scattering, and muon spin rotation/ relaxation techniques. The aim was to correlate the symmetry and structure of the superconducting gap with the unusual properties in these superconductors. These studies have required the preparation of high quality samples using different growth techniques. Good quality polycrystalline and single crystal samples of FeSe1-xTex and FeTe1-xSx were grown using a self- ux method. Polycrystalline samples of Lu2Fe3Si5 and Re3W were made using the arc furnace. We have also grown single crystals of ZrB12 using the optical oating zone method in a 4 mirror image furnace, and CaAlSi crystal using the Bridgman method. All the compounds have been characterized with a combination of X-ray, neutron diffraction, EDX, magnetization, resistivity or specific heat measurements. In order to investigate the pairing symmetry of the iron chalcogenide superconductors, low temperature muon spin rotation/relaxation (μSR) measurements have been performed on FeTe0:5Se0:5. The temperature dependence of the in-plane magnetic penetration depth is found to be compatible with either a two gap s + s- wave or an anisotropic s-wave model. This result is consistent with our heat capacity data collected on the same sample. μSR results of FeTe1-xSx show an antiferromagnetic transition at low temperature and also suggest the presence of excess S in the samples. A similar magnetic transition has also been observed in the magnetization measurements. The symmetry of the superconducting gap of Lu2Fe3Si5 with Tc = 6:1 K has been investigated using low-temperature transverse-field μSR and specific heat measurements. The temperature dependence of the magnetic penetration depth, λ(T) is consistent with a two gap s+s-wave model. Low-temperature specific heat measurements on the same sample also show evidence of two distinct superconducting gaps and hence support the muon results. To resolve whether CaAlSi is a single band or multiband superconductor, we have studied the ux line lattice in CaAlSi using small angle neutron scattering. A well defined hexagonal ux line lattice is seen just above Hc1 in an applied field of only 54 Oe. A 30° reorientation of this vortex lattice has been observed in a very low field of 200 Oe. This reorientation transition appears to be of first-order and could be explained by non-local effects. The magnetic field dependence of the form factor is well described by a single penetration depth and a single coherence length. The penetration depth anisotropy has also been estimated with the field applied at different angles to the c-axis. The B-T phase diagram of superconducting ZrB12 has been investigated by means of μSR spectroscopy using a mosaic of single crystal. The local field distribution for different applied fields and temperatures shows evidence of the Meissner, mixed, and intermediate states in ZrB12. The intermediate state indicates that this material has some of the characteristics of a type-I superconductor, while the mixed state is typical of a type-II superconductor. Regions of coexistence have also been observed between the different states. We have not observed any distinct features of two-band or two-gap superconductivity in this material. Two different superconducting phases of Re3W have been found with different physical properties. One phase crystallizes in a non-centrosymmetric cubic (α-Mn) structure and has a superconducting transition temperature, Tc, of 7.8 K. The other phase has a hexagonal centrosymmetric structure and is superconducting with a Tc of 9.4 K. Switching between the two phases is possible by annealing the sample or remelting it. The zero-field μSR results indicate that time reversal symmetry is preserved for both structures of Re3W. For both phases of Re3W, the temperature dependence of the penetration depth can be explained using a singlegap s-wave BCS model. Low temperature specific heat data also provide evidence for an s-wave gap-symmetry for the two phases of Re3W. Both the μSR and heat capacity data show that the CS material has a higher Tc and a larger superconducting gap (0) at 0 K than the NCS compound. The experimental work detailed in this thesis provides new information on the superconducting properties of FeSe0:5Te0:5, FeTe1-xSx, Lu2Fe3Si5, CaAlSi, ZrB12, and two different superconducting phases of Re3W and contributes to our overall understanding of the physics of the different exotic superconducting features in these systems.