The evolution in the biomedical engineering field boosts innovative technologies, with microfluidic systems standing out as transformative tools in disease diagnosis, treatment, and monitoring. Numerical simulation has emerged as a tool of increasing importance for better understanding and predicting fluid-flow behavior in microscale devices. This review explores fabrication techniques and common materials of microfluidic devices, focusing on soft lithography and additive manufacturing. Microfluidic systems applications, including nucleic acid amplification and protein synthesis, as well as point-of-care diagnostics, DNA analysis, cell cultures, and organ-on-a-chip models (e.g., lung-, brain-, liver-, and tumor-on-a-chip), are discussed. Recent studies have applied computational tools such as ANSYS Fluent 2024 software to numerically simulate the flow behavior. Outside of the study cases, this work reports fundamental aspects of microfluidic simulations, including fluid flow, mass transport, mixing, and diffusion, and highlights the emergent field of organ-on-a-chip simulations. Additionally, it takes into account the application of geometries to improve the mixing of samples, as well as surface wettability modification. In conclusion, the present review summarizes the most relevant contributions of microfluidic systems and their numerical modeling to biomedical engineering.