Bioprinting enables the fabrication of complex, heterogeneous tissues through robotically-controlled placement of cells and biomaterials. It has been rapidly developing into a powerful and versatile tool for tissue engineering. Recent advances in bioprinting modalities and biofabrication strategies as well as new materials and chemistries have led to improved mimicry and development of physiologically relevant tissue architectures constituted with multiple cell types and heterogeneous spatial material properties. Machine learning (ML) has been applied to accelerate these processes. It is a new paradigm for bioprinting. In this review, we explore current trends in bioink formulation and how ML has been used to accelerate optimization and enable real-time error detection as well as to reduce the iterative steps necessary for bioink formulation. We examined how rheometric properties, including shear storage, loss moduli, viscosity, shear-thinning property of biomaterials affect the printability of a bioink. Furthermore, we scrutinized the interplays between yield shear stress and the printability of a bioink. Moreover, we systematically surveyed the application of ML in precision in situ surgical site bioprinting, closed-loop AI printing, and post-printing optimization.