Three-dimensional (3D) cell cultures are increasingly being used in a variety of contexts (e.g., drug discovery, disease modeling, and tissue engineering), as they offer the potential to increase physiological relevance compared to traditional monolayer cultures, while simultaneously reducing cost and time compared to in vivo models. Taking a cue from nature, researchers often create 3D cell cultures using hydrogels that can closely mimic the extracellular matrix that most mammalian cells are surrounded by in vivo. However, aside from the collective physical 3D arrangement itself, the physiology of the culture depends highly on the microenvironment, which is defined by the 3D cell culture shape and the complex combination of biochemical, biophysical, and biomechanical stimuli. Microfluidic devices offer researchers the tantalizing opportunity to precisely define and influence this microenvironment. Furthermore, they additionally enable the integration of external functional components for active stimulation and monitoring of cultured cells. Pushing for ever-more-realistic culture conditions has, however, increased the complexity that is required of these microfluidic culture systems, making their fabrication more difficult. In this regard, 3D printing is becoming an increasingly popular solution, as it offers researchers not only the ability to fabricate highly complex structures but also to benefit from rapid prototyping and customization of existing designs. This review discusses common challenges that researchers currently face when integrating hydrogel-embedded cells into 3D-printed microfluidic cell culture devices and seeks to offer a comprehensive overview of recent advancements aimed at addressing these challenges.