In recent years, Raman spectroscopy has undergone major advancements in its ability to probe deeply through turbid media such as biological tissues. This progress has been facilitated by the advent of a range of specialist techniques based around spatially offset Raman spectroscopy (SORS) to enable non-invasive probing of living tissue through depths of up to 5 cm. This represents an improvement in depth penetration of up to two orders of magnitude compared to what can be achieved with conventional Raman methods. In combination with the inherently high molecular specificity of Raman spectroscopy, this has therefore opened up entirely new prospects for a range of new analytical applications across multiple fields including medical diagnosis and disease monitoring. This article discusses SORS and related variants of deep Raman spectroscopy such as transmission Raman spectroscopy (TRS), micro-SORS and surface enhanced spatially offset Raman spectroscopy (SESORS), and reviews the progress made in this field during the past 5 years including advances in non-invasive cancer diagnosis, monitoring of neurotransmitters, and assessment of bone disease.