In an extended introduction, key aspects of resonance Raman spectroscopy (RRS) such as enhanced sensitivity and selectivity are briefly discussed in comparison with normal RS. The analytical potential is outlined. Then achievements in different fields of research are highlighted in four sections, with emphasis on recent breakthroughs: (1) The use of visible RRS for analyzing carotenoids in biological matrices, for pigments and dyes as dealt with in art and forensics, and for characterizing carbon nanotubes. (2) The use of RRS in the deep UV (excitation below 260nm) in the bioanalytical and life sciences fields, including nucleic acids, proteins and protein-drug interactions. Metalloproteins can be studied by visible RRS in resonance with their chromophoric absorption. (3) Progress in theoretical calculations of RRS excitation profiles and enhancement factors, which ultimately might facilitate analytical RRS. (4) Instrumental and methodological achievements including fiber-optic UV-RRS, coupling of RRS to liquid chromatography and capillary electrophoresis. Sensitivities can approach the single-molecule level with surface-enhanced RRS or tip-enhanced RRS. Last but not least, promising fluorescence background rejection techniques based on time-gated detection will be presented. This review ends with a concluding section on future expectations for RRS, in particular its potential as an analytical technique.