Oppositely-charged macromolecules can undergo an associate phase separation, in a process known as complex coacervation. In this process, any combination of macromolecular species, including colloidal particles, proteins, surfactants, and polymers, 1 can form a dense 'coacervate' phase that maximizes favorable electrostatic interactions and a dilute 'supernatant' phase that is composed mostly of solvent and small-molecule salt ions. This macroscopic phase separation was first identified in 1929 by Bungenberg de Jong and Kruyt, and since then there has been sustained progress in our understanding of these materials. This has been spurred in large part by their relevance to food science and personal care products, where coacervates are used as viscosity modifiers and encapsulants, and can be made using biopolymers. Recently, however, there has been a surge of interest in coacervation, driven by their promise as a biomaterial for protein encapsulation and as an analogue to help understand liquid-liquid phase seperation phenomena in cells. This has led to a large number of fundamental experimental studies, probing the thermodynamics and structure of coacervates, with a particular focus on coacervates formed between oppositely-charged polyelectrolytes. These experiments have established some of the first comprehensive phase diagrams mapping out a rather large parameter space, seeking to understand the role of chain length, salt concentration, polymer concentration, polarity, stoichiometry, chain flexibility, valency, temperature, monomer sequence, crowding, and pH. Systematic study of this wide variety of parameters has facilitated the use of coacervates in self-assembly, 46-55 drug delivery, and other materials applications. A wide range of characterization methods have been used in pursuit of understanding phase behavior, including turbidity measurements, thermogravi-metric analysis, and fluorescence. This has been coupled with isothermal titration calorimetry to understand coacervation thermodynamics and scattering to understand polymer structure. Concomitant with experimental efforts to understand complex coacervates, theory and simulation have been used to provide molecular interpretation and insight into the physical origins of phase separation. The earliest example, which remains a commonly-used model for coacervation, is the Voorn-Overbeek model. This original model combined the Flory-Huggins theory of polymer solutions with the Debye-Hückel theory of dilute electrolytes to establish a free energy expression that can predict coacervation. We will discuss this model in more detail later, but importantly it captures much of the phenomenology of coacervation; phase separation is observed at low salt and polymer concentrations, where electrostatic interactions are weakly screened, while the system is miscible at high salt and polymer concentrations. With certain choices of the model parameters, it is possible to fit standard phase diagrams. Beyond phase separation, this model has been used in predictions for interfacial tension, ion partitioning, and as a way to explain time-salt superposition in rheological measurements. Despite the successful features of Voorn-Overbeek, it is now accepted that it neglects several important physical features. This is unsurprising, as the Debye-Hückel model does not account for the connected nature of the polyelectrolytes, is limited to dilute electrolyte concentrations, and neglects the finite volume of the polymer and salt species. This means that the parameters used to match Voorn-Overbeek to experimental phase diagrams generally lack physical meaning. Subsequent theoretical modeling has sought to develop a more sophisticated physical picture of coacervation, 1 with most theories addressing some or all of these issues. In this effort, there has been a proliferation of possible coacervate models, building on the various theoretical approaches common in the field of polymer physics. Most connected to Voorn-Overbeek, polymer field theory has been widely used to include the effects of connectivity and the effects of fluctuating charge. Simplified representations of excluded volume are considered in several of these models, though typically relying on (for example) Gaussian-smeared distributions of charged species. Relatedly, scaling theory is also used to capture key length scales associated with electrostatic interactions and polymer conformations, including connectivity but requiring ad hoc modifications to describe highly correlated electrolytes. Liquid state theory is a traditional way to addressing these strong correlations in charged systems, and has been used to predict coacervate phase behavior; however, the use of complicated closure relationships limits the practical application of these models beyond simple homopolyelectrolyte coacervates. Finally, ion pairing theory is a broad class of models that uses simplified arguments to account for these same correlations, but has to this point been largely accounted for in an ad hoc fashion. This includes both 'effective' ion pairing or binding reactions, and the transfer matrix model developed by the authors. Taken as a whole, these theoretical approaches all provide a coherent picture of coacervation, though each method has its own limits of applicability. A key variable in this regard is the linear charge density, which affects the strength of charge correlations (e.g. such as those related to counterion condensation), indirectly sets the overall density of charged species, and governs the putative mechanism of coacervation. Generally speaking, polymer field theory and scaling theory exhibit fluctuation-driven coacervation, where attractions are governed by Gaussian chain statistics between widely-spaced charged monomers. Conversely, liquid state and ion pairing theories rely on interactions governed by strong correlations between tightly connected charged monomers. Evidence in both experiments and simulations support this distinction, and has prompted efforts to either include correlations into field/scaling theories or to include fluctuating chain statistics into ion pairing theories. 100,109 Despite progress, however, the formal differences between these various approaches frustrates attempts at comparison or consolidation. This is exacerbated by another major factor; experiment is not always discerning, as most coacervate theories at least provide plausible phase diagrams and correct trends, with differences easily (and often correctly) attributed to the specific chemistries used in a given experiment. This means that most theoretical approaches have some successful experimental comparison to support their method. This is positive, in that theorists in the field are working in close concert with experimental collaborators, but can muddle the advantages and disadvantages of the various approaches. There is thus a need to establish a shared theoretical basis that can clarify the approximations inherent to each approach.