Recent advances in bioprinting technologies have enabled rapid manufacturing of organ-on-chip models along with biomimetic tissue microarchitectures. Bioprinting techniques can be used to integrate microfluidic channels and flow connections in organ-on-chip models. We review bioprinters in two categories of nozzle-based and optical-based methods, and then discuss their fabrication parameters such as resolution, replication fidelity, fabrication time, and cost for micro-tissue models and microfluidic applications. The use of bioprinters has shown successful replicates of functional engineered tissue models integrated within a desired microfluidic system, which facilitates the observation of metabolism or secretion of models and sophisticated control of a dynamic environment. This may provide a wider order of tissue engineering fabrication in mimicking physiological conditions for enhancing further applications such as drug development and pathological studies.