Many physicists see biology as very complex and messy, and often it is. Certain problems in biology, though, serve as an elegant playground for physicists to develop quantitative AND predictive models. For example, problems in biology in which cells generate forces to perform some function allow physicists to make ourselves useful to biologists, our collaborators. In this talk, I will take you on a journey from the retinae of juvenile zebrafish to the outer tissue layer of developing mammalian embryos. In juvenile zebrafish, the cone photoreceptors in retinae form a precise crystalline lattice based on subtype (i.e., sensitivity to different wavelengths of light). We find that the defects in this lattice form lines, called grain boundaries, as the pattern forms, not by subsequent defect motion. Based on this observation, we propose a model in which cells of fixed fate (i.e., subtype) contact their neighbors of the same subtype, generating active forces for building the crystal. From there, I will take you to an example in which cell fate is not fixed. In this stem cell culture system, without any imposed chemical gradients and in the absence of many known endogenous gradients, cells of initially unspecified fate differentiate into two types, with one type localized to a ring at the boundary. We propose a model for this system in which mechanical stress biases fate and fate determines contractility. The role of cell-cell contacts and mechanics in pattern formation in developing tissues remains poorly understood. Luckily for us physicists, these problems provide endless intellectual stimulation.