In this paper we present an overview of some key theoretical tools employed for the investigations of the equilibrium structure and thermodynamics of complex fluids. We place our focus on the most common systems of soft-matter science, namely dispersions of colloidal particles, which may be hard or soft, and which may carry electric charge. The concept of the effective Hamiltonian, which plays the key role in these coarse-grained approaches is introduced, and it is given a precise mathematical definition. Its properties as well as key approximations involved in deriving effective potentials are discussed. Thereafter, the ways in which the effective interactions can be combined with tools from the theory of fluids and statistical mechanics are presented, putting emphasis on Density Functional Theory. The general principles are combined with extensive exposures from currently active research fields, and applications to interfacial and wetting behavior of complex mixtures as well as to crystallization and cluster formation are discussed. Appendix A serves as a mini-course on functionals and functional differentiation.