Ocean wind and wave parameters can be measured by in-situ sensors such as anemometers and buoys. Since the 1980s, X-band marine radar has evolved as one of the remote sensing instruments for such purposes since its sea surface images contain considerable wind and wave information. The maturity and accuracy of X-band marine radar wind and wave measurements have already enabled relevant commercial products to be used in real-world applications. The goal of this paper is to provide a comprehensive review of the state of the art algorithms for ocean wind and wave information extraction from X-band marine radar data. Wind measurements are mainly based on the dependence of radar image intensities on wind direction and speed. Wave parameters can be obtained from radar-derived wave spectra or radar image textures for non-coherent radar and from surface radial velocity for coherent radar. In this review, the principles of the methodologies are described, the performances are compared, and the pros and cons are discussed. Specifically, recent developments for wind and wave measurements are highlighted. These include the mitigation of rain effects on wind measurements and wave height estimation without external calibrations. Finally, remaining challenges and future trends are discussed.