Since the first reports on high efficiency, solution processed solar cells based on hybrid lead halide perovskites, there has been an explosion of activities on these materials. Researchers with interests spanning the full range from conventional inorganic to emerging organic and hybrid optoelectronic technologies have been contributing to the prolific research output. This has led to solar cell power conversion efficiencies now exceeding 20% and the demonstration of proofs of concept for electroluminescent and lasing devices. Hybrid perovskites can be self-assembled by a simple chemical deposition of the constituent units, with the possibility of integrating the useful properties of organic and inorganic compounds at the molecular scale within a single crystalline material, thus enabling a fine-tuning of the electronic properties. Tellingly, the fundamental properties of these materials may make us think of a new, solution processable, GaAs-like semiconductor. While this can be true to a first approximation, hybrid perovskites are intrinsically complex materials, where the presence of various types of interactions and structural disorder may strongly affect their properties. In particular, a clear understanding and control of the relative interactions between the organic and inorganic moieties is of paramount importance to properly disentangle their innate physics. In this Account we review our recent studies which aim to clarify the relationship between structural and electronic properties from a molecular to mesoscopic level. First we identify the markers for local disorder at the molecular level by using Raman spectroscopy as a probe. Then, we exploit such a tool to explore the role of microstructure on the absorption and luminescence properties of the semiconductor. Finally we address the controversy surrounding electron-hole interactions and excitonic effects. We show that in hybrid lead-halide perovskites dielectric screening also depends on the local microstructure of the hybrid crystals and not only on its chemical composition. This leads to the possibility of band gap engineering and the consequent control of the elementary photoexcitation dynamics that determine the perovskites' performances in different optoelectronic devices.