Extrusion-based 3D printers have been adopted in pursuit of engineering functional tissues through 3D bioprinting. However, we are still a long way from the promise of fabricating constructs approaching the complexity and function of native tissues. A major challenge is presented by the competing requirements of biomimicry and manufacturability. This opinion article discusses 3D printing in suspension baths as a novel strategy capable of disrupting the current bioprinting landscape. Suspension baths provide a semisolid medium to print into, voiding many of the inherent flaws of printing onto a flat surface in air. We review the state-of-the-art of this approach and extrapolate toward future possibilities that this technology might bring, including the fabrication of vascularized tissue constructs. 3D printing in suspension media unlocks the full potential of extrusion-based 3D printers by providing a strategy for fabricating non–self-supporting structures from water-rich, low-viscosity bioinks.Biomimetic structures representative of native vascular channels have been printed in suspension media, demonstrating that both omnidirectional printing and printing in discrete arbitrary locations are possible with this printing strategy.Retention of a suspension medium following printing of embedded constructs is achievable through crosslinking. Suspension media are therefore able to double as a 3D cell culture substrate in which printed features such as vessels or cell populations can help with maturing of the engineered tissue.