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### Abstract

One characterization of human scientific and industrial development is in terms of the increasing ability to control the physical world at smaller and smaller length scales. As control has increased, we have advanced from chemistry, to nuclear physics, to particle accelerators. But control over individual particles is different from control over many~\cite{Anderson72}. In this work, we study how particles of size between nanometers and micrometers, called colloids or solutes, interact within complicated solvent systems (or soft matter'' fluids). Our goal is to learn how to design colloids and fluids such that we can control their properties, such as the solubility of colloids within the fluid, or the shapes of fluid droplets that associate with the colloid. In particular, for a large part of this work, we are motivated by recent studies of colloids and surfaces within molten salts and ionic liquids that defy theoretical explanation to this day. To work towards an explanation, we search for the key elements that are required to reproduce the observed phenomena: the minimal model to describe experiment. In addition to simple theoretical models, we extend the applicability of our work through molecular and coarse-grained computer simulation. In this work, we first introduce some foundational theories of fluids and ionic solutions that we will return to throughout this work. Motivated by recent unexplained experimental results on high ionic strength solutions, we apply some of these theoretical tools to a lattice model, the charge-frustrated Ising model, which we use to generalize past models of dilute ionic solutions to solvents with high ionic strength. This model helps us to frame the next two studies that we detail, which examine the unexpected experimental observation that nanocrystal colloids do not precipitate out of solution in molten salts and ionic liquids, ie. are colloidally stable''. Though our mean field model and molecular dynamics simulations, are able to explain the majority of the experimental observations in these works, some questions still remain. Next, changing focus, we examine another colloid-soft matter system, in which a colloid is able to affect shape changes upon nematic liquid crystal droplets. We provide a set of predictions about the requirements for a colloid and fluid to have such dramatic shape changes as the stable division of fluid droplets. The connecting thread between these works is our attention to the minimal features necessary to describe these complex fluids with long-range interactions. We are continually surprised at the effectiveness of these simple models at capturing complex physical phenomenology.