We review state-of-the-art computational methods for constructing, from image data, generative statistical models of cellular and nuclear shapes and the arrangement of subcellular structures and proteins within them. These automated approaches allow consistent analysis of images of cells for the purposes of learning the range of possible phenotypes, discriminating between them, and informing further investigation. Such models can also provide realistic geometry and initial protein locations to simulations in order to better understand cellular and subcellular processes. To determine the structures of cellular components and how proteins and other molecules are distributed among them, the generative modeling approach described here can be coupled with high throughput imaging technology to infer and represent subcellular organization from data with few a priori assumptions. We also discuss potential improvements to these methods and future directions for research.