The invention relates to devices and methods for growing cells in vitro in an enclosed device that allows for a three-dimensional measurement over time of both their proliferative and/or invasive properties. By growing the cells in an enclosed matrix that resembles the environment that the cells confront in vivo, the cells can divide, invade, and form branched networks as they do in living tissue, e.g., in an individual. The devices of the invention include a test chamber in which cells, e.g., tumor cells, are placed and permitted to divide and/or invade. Cells can be placed within an insert within a chamber of the device. A delivery chamber that connects to the test chamber enables the delivery of agents that can be studied, e.g., for their therapeutic potential. The assay devices of the invention can be used as model systems to study cancer biology and to evaluate the efficacy of anti-cancer therapeutics.