This thesis deals with several problems in condensed matter theory involving strong correlations and/or a disorder. It is divided into four parts, with the effects of electron-phonon interaction appearing as the key subject of the first three parts. The focus of the last part is on the role of strong disorder in strongly correlated systems. In the first part, we provide the exact solution to the polaronic impurity problem and exploit it to study some aspects of local and transport properties in systems with dilute concentrations of polaronic impurities. We find a non-universal power-law decay of the electron mobility with temperature in bulk systems, which may be relevant for rationalizing the unconventional power-law exponents observed in organic semiconductors. In the next step, the translational invariance of the electron-phonon system is restored. In the second part, we perturbatively address the polaron problem. We show that the leading order momentum-dependent electron self-energy becomes suppressed in the antiadiabatic limit. We argue that the polarization may be treated within the two-vertices renormalization scheme, with vertex corrections involving electron processes only. Several experimental findings are analyzed by simulating angle-resolved photoemission spectroscopy (ARPES), electron energy loss spectroscopy, and phonon spectra for cases of strongly doped polar semiconductors in the third part. We show that ARPES spectra can provide a robust estimate of the electron-phonon interaction range. Emphasis is placed on the importance of the coupling strength in shaping both raw and integrated spectra of phonon-plasmon coupled systems. In the last part of the thesis, we consider the very interesting phenomenon of many-body localization (MBL). We argue that the change from the thermal to the MBL phase may be thought of as a percolation transition in the Fock space, with the anomalous transport behaviors characterizing the large portion of the thermal phase.