Micron-scale computed tomography (micro-CT) is an essential tool for phenotyping and for elucidating diseases and their therapies. This work is focused on preclinical micro-CT imaging, reviewing relevant principles, technologies, and applications. Commonly, micro-CT provides high-resolution anatomic information, either on its own or in conjunction with lower-resolution functional imaging modalities such as positron emission tomography (PET) and single-photon emission computed tomography (SPECT). More recently, however, advanced applications of micro-CT produce functional information by translating clinical applications to model systems (e.g. measuring cardiac functional metrics) and by pioneering new ones (e.g. measuring tumor vascular permeability with nanoparticle contrast agents). The primary limitations of micro-CT imaging are the associated radiation dose and relatively poor soft tissue contrast. We review several image reconstruction strategies based on iterative, statistical, and gradient sparsity regularization, demonstrating that high image quality is achievable with low radiation dose given ever more powerful computational resources. We also review two contrast mechanisms under intense development. The first is spectral contrast for quantitative material discrimination in combination with passive or actively targeted nanoparticle contrast agents. The second is phase contrast which measures refraction in biological tissues for improved contrast and potentially reduced radiation dose relative to standard absorption imaging. These technological advancements promise to develop micro-CT into a commonplace, functional and even molecular imaging modality.