Transport properties in strongly correlated quantum materials are frequently the focal point of experimental scrutiny, yet they pose some of the deepest mysteries in the field. The seemingly intertwined nature of unconventional transport and high-temperature superconductivity in many materials underscores the necessity for further inquiry into both phenomena. Central to these issues is the breakdown of the Landau-quasiparticle picture, which forms the conventional approach to the many-body problem in Fermionic quantum systems. Signatures of this breakdown manifest in what has been termed bad-metallic and Planckian transport in numerous strongly correlated compounds. These phenomena correspond to scenarios where the mean free path for transport is inconsistent with the existence of Landau quasiparticles, and where the transport scattering rate appears to be universally bounded in certain classes of correlated materials. In this thesis, we address both phenomena in specific cases. For bad-metallic transport, we analyze a toy model of interacting electrons on a frustrated lattice and, utilizing a strong-coupling approach, we describe transport in this system beyond the Boltzmann paradigm. For Planckian transport, we present a phenomenological description of two sister compounds within the delafossite family, PdCrO$_2$ and PdCoO$_2$. We explore the puzzling observation that despite their similar electronic and phononic spectra, PdCrO$_2$ seemingly exhibits a scattering rate that saturates the Planckian bound, while PdCoO$_2$'s transport properties can be fully explained within conventional Boltzmann transport theory. Additionally, we indirectly address the problem of strong-coupling superconductivity in twisted bilayer graphene (TBG). By leveraging an emergent optical sum rule in the flat-band projected limit of TBG, we start from the strong-coupling limit to calculate a heuristic bound on the superfluid stiffness. By examining this procedure in the vicinity of various candidate correlated insulating states, we illuminate the properties of the underlying ground states that lead to increased spectral weight, which could subsequently enhance $T_c$.