The discovery of high temperature superconductivity in the cuprates in 1986 has boosted the research in strongly correlated materials. One strong motivation was and stays the understanding the high-Tc phenomenon with the hope that one can ultimately engineer new materials with even higher Tc. Besides the in-depth investigation of cuprates, there is a strong tendency in the solid state community to find new superconductors, which by themselves are interesting for applications, or by their properties they can contribute to the understanding of the high-Tc phenomenon. The program of my doctoral thesis was three-fold: i) to address one important issue in the cuprate superconductors, that of the role of homogeneity in the underdoped part of the phase diagram; ii) what is the effect of disorder in MgB2 superconductor, which has high potentials for applications; iii) to discover new superconductors in the family of transition metal dichalcogenides. All these materials are in some sense unconventional superconductors. The cuprates by their high Tc and the symmetry of the order parameter, MgB2 by its two-band superconductivity and Tc of 39 K, and the dichalcogenides by the appearance of superconductivity on the background of competing interactions. Measurements of transport properties, such as resistivity and thermoelectric power, were used to get insight in the behavior of these materials. Besides temperature as variable, I applied high pressure, extreme magnetic fields and controlled disorder introduced by fast electron irradiation. In the first part I present the pressure dependent study of two members of the transition metal dichalcogenides having 1T structure, 1T-TiSe2 and 1T-TaS2, where superconductivity was never observed in a pristine sample. 1T-TiSe2 has a CDW phase below 220 K which origin, weather it is driven by an excitonic mechanism or by a Jahn-Teller distortion, is an ongoing question. By applying pressure I showed that the pristine sample is superconducting in the pressure range of 2.0–4.0 GPa. This range remarkably coincides with the short range fluctuating CDW before its disappearance at the upper pressure value. If CDW is due to excitonic interactions than our observations suggest that it can be at the origin of superconductivity, as well. The second dichalcogenide is the 1T-TaS2, where a Mott-insulator phase appears on the top of a commensurate CDW. By applying pressure I was able to melt that Mott-phase, and reveal that the material is superconducting above 2.5 GPa with Tc of 5.9 K. Unexpectedly, superconductivity is born from a nonmetallic phase, and stays remarkably stable up to the highest applied pressure of 24 GPa. In the second part I tried to give my contribution to the field of high-Tc superconductors. I carefully selected few high quality underdoped Bi2Sr2PrxCa1-xCu2O8-δ sample, to address the nature of the low temperature ground state by applying high magnetic field. Although former measurements by other groups showed that at high underdoping, the ground state is an insulator, I found that a sample with as low Tc as 15 K exhibits metallic behavior up to 60 T. Furthermore, I showed that a inhomogeneous distribution of the doping atoms can completely mask the intrinsic normal state of a high-Tc superconductor. In the last part of my thesis I focused on the two-band superconductor MgB2 by studying the scattering between the bands by the means of the Matthiessen's rule. I made a systematic study of the influence of defects created by fast electron irradiation, and found that the the Matthiessen's rule is satisfied for the defect concentration range I induced. I further compare the influence of defects on the critical temperature and the residual resistivity in MgB2 with superconductors with various order parameters, and found that the decrease-rate of Tc in our system is within the range of a response of a superconductor with an s-wave order parameter.