The blood–brain barrier (BBB) is responsible for maintaining homeostasis within the central nervous system (CNS). Depending on its permeability, certain substances can penetrate the brain, while others are restricted in their passage. Therefore, the knowledge about BBB structure and function is essential for understanding physiological and pathological brain processes. Consequently, the functional models can serve as a key to help reveal this unknown. There are many in vitro models available to study molecular mechanisms that occur in the barrier. Brain endothelial cells grown in culture are commonly used to modeling the BBB. Current BBB platforms include: monolayer platforms, transwell, matrigel, spheroidal, and tissue-on-chip models. In this paper, the BBB structure, molecular characteristic, as well as its dysfunctions as a consequence of aging, neurodegeneration, or under hypoxia and neurotoxic conditions are presented. Furthermore, the current modelling strategies that can be used to study BBB for the purpose of further drugs development that may reach CNS are also described.