Lensfree on-chip holographic microscopy is an emerging technique that offers imaging of biological specimens over a large field-of-view without using any lenses or bulky optical components. Lending itself to a compact, cost-effective, and mechanically robust architecture, lensfree on-chipholographic microscopy can offer an alternative toolset addressing some of the emerging needs of microscopic analysis and diagnostics in low-resource settings, especially for telemedicine applications. In this study, we summarize the latest achievements in lensfree optical microscopy based on partially coherent on-chip holography, including portable telemedicine microscopy, cell-phone-based microscopy, and field-portable opticaltomographic microscopy. We also discuss some of the future directions for telemedicine microscopy and its prospects to help combat global healthchallenges.