The recent revolution in digital technologies and information processing methods present important opportunities to transform the way optical imaging is performed, particularly toward improving the throughput of microscopes while at the same time reducing their relative cost and complexity. Lensfree computational microscopy is rapidly emerging toward this end, and by discarding lenses and other bulky optical components of conventional imaging systems, and relying on digital computation instead, it can achieve both reflection and transmission mode microscopy over a large field-of-view within compact, cost-effective and mechanically robust architectures. Such high throughput and miniaturized imaging devices can provide a complementary toolset for telemedicine applications and point-of-care diagnostics by facilitating complex and critical tasks such as cytometry and microscopic analysis of e.g., blood smears, Pap tests and tissue samples. In this article, the basics of these lensfree microscopy modalities will be reviewed, and their clinically relevant applications will be discussed.