This thesis (Electrical transport and superconductivity in doped quantum critical ferroelectrics) presents the results of research into the electrical transport and superconductivity found in the neighbourhood of quantum phase transitions in carrier-doped ferroelectrics and paraelectrics. The materials of interest are doped SrTiO3, located close to the quantum critical point at ambient pressure and doped ferroelectric BaTiO3, which may be tuned to its quantum phase transition with hydrostatic pressure. In the project of carrier-doped SrTiO3, we observed unconventional resistivity varying as the square of the temperature at ambient pressure, which is not thought to be attributed to conventional Fermi-liquid electron-electron scattering. The results of resistivity measured under high pressure are presented which indicate a potential relation to quantum criticality. A theoretical model is presented based on the idea that electrons can scatter from fluctuations of the polarization-squared field which are also known as 'energy' or 'two-phonon' fluctuations. The model seems to find quantitative agreement with the high-pressure resistivity measurements as well as recently published thermal conductivity data. We also further investigated the enhanced superconductivity of carrier-doped SrTiO3 around the quantum critical point by high-pressure measurements in samples of varying charge carrier densities. Our data provided further evidence in support of the so-called hybrid-polar-mode mechanism of superconductivity. Although the second candidate, carrier-doped BaTiO3, is far away from the quantum critical point, we used a high-pressure moissanite anvil cell to tune oxygen-reduced specimens near to the quantum phase transition with carrier densities similar in range to those in superconducting SrTiO3. We succeeded in making semiconductive and metallic BaTiO3 samples with ferroelectricity retained. We did not detect clear evidence of superconductivity of oxygen-reduced BaTiO3 so far at the particular pressure points investigated.