Phenolic compounds have recently gained interest, as they have been related to improvements in health and disease prevention, such as inflammatory intestinal pathologies and obesity. However, their bioactivity may be limited by their instability or low concentration in food matrices and along the gastrointestinal tract once consumed. This has led to the study of technological processing with the aim of optimizing phenolic compounds’ biological properties. In this sense, different extraction systems have been applied to vegetable sources for the purpose of obtaining enriched phenolic extracts such as PLE, MAE, SFE, and UAE. In addition, many in vitro and in vivo studies evaluating the potential mechanisms of these compounds have also been published. This review includes a case study of the Hibiscus genera as an interesting source of phenolic compounds. The main goal of this work is to describe: (a) phenolic compound extraction by designs of experiments (DoEs) applied to conventional and advanced systems; (b) the influence of the extraction system on the phenolic composition and, consequently, on the bioactive properties of these extracts; and (c) bioaccessibility and bioactivity evaluation of Hibiscus phenolic extracts. The results have pointed out that the most used DoEs were based on response surface methodologies (RSM), mainly the Box–Behnken design (BBD) and central composite design (CCD). The chemical composition of the optimized enriched extracts showed an abundance of flavonoids, as well as anthocyanins and phenolic acids. In vitro and in vivo studies have highlighted their potent bioactivity, with particular emphasis on obesity and related disorders. This scientific evidence establishes the Hibiscus genera as an interesting source of phytochemicals with demonstrated bioactive potential for the development of functional foods. Nevertheless, future investigations are needed to evaluate the recovery of the phenolic compounds of the Hibiscus genera with remarkable bioaccessibility and bioactivity.