Significant strides have been made in the development of in vitro systems for disease modelling. However, the requirement of microenvironment control has placed limitations on the generation of relevant models. Herein, we present a biological tissue printing approach that employs open-volume microfluidics to position individual cells in complex 2D and 3D patterns, as well as in single cell arrays. The variety of bioprinted cell types employed, including skin epithelial (HaCaT), skin cancer (A431), liver cancer (Hep G2), and fibroblast (3T3-J2) cells, all of which exhibited excellent viability and survivability, allowing printed structures to rapidly develop into confluent tissues. To demonstrate a simple 2D oncology model, A431 and HaCaT cells were printed and grown into tissues. Furthermore, a basic skin model was established to probe drug response. 3D tissue formation was demonstrated by co-printing Hep G2 and 3T3-J2 cells onto an established fibroblast layer, the functionality of which was probed by measuring albumin production, and was found to be higher in comparison to both 2D and monoculture approaches. Bioprinting of primary cells was tested using acutely isolated primary rat dorsal root ganglia neurons, which survived and established processes. The presented technique offers a novel open-volume microfluidics approach to bioprint cells for the generation of biological tissues.