Molecular orbitals (MOs) in inorganic crystalline solids arise as a peculiar result of an intricate interplay between structural geometry, favourable hierarchies of hybridization pathways, and strong local electronic correlations. When involved in low-energy physics, MOs often give rise to intriguing physical effects, expanding experimentally accessible regions of quantum phase diagrams and providing new ways to tune material properties. In this talk, I will present two examples of quantum MO systems: (1) Ti_4 MnBi_2, a one dimensional metallic spin-½ system, and (2) La_3 Ni_2 O_7, a member of the most recently discovered Ni-based family of high-temperature superconductors. Using these examples, I will attempt to not only illustrate the rich physics of MOs in action but also highlight the challenges that such systems pose at various levels of condensed matter theory, from ab initio electronic structure calculations to model-based and analytical approaches.