This paper reviews the main results of the study, carried out in the framework of the Italian National Institute of Nuclear Physics (INFN, Istituto Nazionale di Fisica Nucleare) projects, namely CANDIDO and CONRAD, on natural and synthetic diamond-based dosimeters for clinical radiotherapy. Characteristics of diamond such as radiation hardness, high sensitivity, tissue equivalence, etc., make this material interesting for dosimetry applications. For some years, natural diamonds have been commercially available for on-line radiotherapy dosimetry. Nevertheless, recent developments in the "Chemical Vapour Deposition" (CVD) technique have addressed the attention on synthetic samples that potentially could be grown at low cost and with features suitable for dosimetric use. Several samples, differently grown and with different electrical contacts, have been compared by measuring their current response during irradiation with high-energy photon, electron and proton beams. Properties of dosimetric interest such as linearity, pre-irradiation dose, dose rate dependence, stability and rise time have been investigated. The results obtained so far within the INFN collaboration demonstrate the suitability of natural diamond detectors for many radiotherapy applications and the great potential of CVD diamond-based devices even though, at present, the commercial natural diamond dosimeters have a better behaviour with respect to the synthetic samples. Further efforts have to be made mainly to improve the dynamic of response and performance stability.