Membrane-less organelles are cellular structures which arise through the phenomenon of phase separation. This process enables compartmentalization of specific sets of macromolecules (e.g., proteins, nucleic acids), thereby regulating cellular processes by increasing local concentration, and modulating the structure and dynamics of their constituents. Understanding the connection between structure, material properties and function of membrane-less organelles requires inter-disciplinary approaches, which address length and timescales that span several orders of magnitude (e.g., Ångstroms to micrometer, picoseconds to hours). In this review, we discuss the wide variety of methods that have been applied to characterize the morphology, rheology, structure and dynamics of membrane-less organelles and their components, in vitro and in live cells.