Over the past few decades colloidal chemistry has provided access to a growing variety of inorganic nanostructures with diverse and customizable properties, which can be tailored to many different applications. However, such diversity presents challenges when it comes to characterizing the structure of functional nanomaterials, where the small size and the increased complexity impose technical limitations.This Thesis aims to address these challenges by developing novel approaches to characterize and describe the structure of nanomaterials, which are here demonstrated on lead halide semiconductor nanostructures. These materials are widely investigated for their appealing properties and the structural diversity they express at the nanoscale, and pose therefore a variety of compelling scientific questions. Here are discussed four case studies, each characterized by increasing nanoscale complexity. I) Colloidal nanocrystals of previously unknown lead chalcohalide phases are used to demonstrate strategies for solving the structure of novel inorganic materials by means of combined electron and X-ray diffraction techniques. Guidelines are proposed for each step of the structure solution process, from the stoichiometry determination to the cell indexation and the final structure refinement.II) Epitaxial dimers formed by cesium lead halide compounds are rationalized as reaction intermediates in the chemical transformation of colloidal nanocrystals, and the structural relationships enabling their formation are explored. Following this lead, perovskite/chalcohalide heterostructures are demonstrated as effective templates for the phase-selective synthesis of colloidal nanocrystals. III) Superlattices of lead halide perovskite nanocrystals are used to develop a novel approach for characterizing the nanoscale structure of self-assembled nanocrystal solids. This method is based on diffraction techniques developed for multilayer thin films grown by physical methods, and relies on the analysis of collective interference phenomena in the wide-angle X-ray diffraction pattern of samples.IV) Microcrystalline samples of hybrid layered Ruddlesden-Popper perovskites, composed by nanoscale stacks of organic and inorganic layers, are investigated through a geometric analysis of their unit cell parameters to determine the inhomogeneous distribution of different halides alloyed within their structure.