Recently, the bioactive potential of several functional ingredients and biomolecules has been evaluated regarding human and animal nutrition. The digestive process from food intake to absorption and metabolism are important events that induce changes in ingredients, which affect their bioactivity. Consequently, there is a need to assess the bioavailability and bioaccessibility of these compounds. The methodology for the simulation of the human gastrointestinal tract has been standardized (INFOGEST protocol), while a gastrointestinal protocol for other animals (e.g., ruminants or broilers) has yet to be established. However, INFOGEST allows us only to predict bioaccessibility, leaving a gap regarding a methodology able to assess bioavailability by mimicking intestinal permeability and absorption. Several approaches—including in vitro, ex vivo, in situ and in vivo methods—can be found in the literature, aiming to tackle transepithelial routes, but leading to different results concerning the bioefficiency of the compounds studied. Therefore, this review aims to assess the current state-of-the-art regarding monogastric intestinal dynamics, absorption, and permeability events. Moreover, it compiled methodologies for simulating intestinal absorption in several biological systems, while reasoning their advantages, disadvantages, applications in ingredient development and the existing gaps.