Fundamental and applied research on supercritical fluid (SCF) technology is of importance in successfully developing applications in many industrial arenas. The success of this technology is reflected in the several applications developed to date in the food, pharmaceutical, textile, waste treatment, precision and garment dry cleaning, and petroleum industries. To identify several more potential applications, experimental and computational studies provide well-founded tools that allow a deeper understanding of the nature of fluids in the supercritical state. Among all the wide variety of interesting studies that can emerge from this technology, we focused on three main concerns to obtain a better insight into SCF's: (1) the computational study of high-pressure chemical and multiphase equilibrium and the importance of mathematical validation of the number of phases and composition after reaction, (2) the experimental and modeling of solubilities of solutes in SCF's, and (3) the design and optimization of supercritical extraction processes (SFE). First we present V-CHASEOS, a validated computational tool that correctly estimates the number of phases and compositions of reacting and non-reacting systems in equilibrium. Our methodology takes good advantage of the wealth of techniques that combined with the interval methodology validates correct results, identifies incorrect results, and provides a corrective feedback until a correct answer is found. Five sample cases are presented to highlight the benefits of this methodology. For the second part, the solubility of three compounds of pharmaceutical and biochemical importance (caffeine, uracil and erythromycin) in supercritical CO2 were studied. Solid-fluid equilibrium curves are modeled according to the Peng-Robinson Equation of State (PR EOS) and compared to the experimental results. Different parameter estimation techniques are also studied. Finally, a computational method for the optimization of SFE processes is studied. We implement a process synthesis technique called Generalized Modular Framework (GMF) that systematically allows, without prepostulation of unit operations, the determination of optimum process schemes based on multifunctional mass/heat transfer-based process modules. As a sample case, optimization of the recovery of solutes from a substrate containing anthracene, phenanthrene and benzoic acid using supercritical CO2 is presented.