The article focuses on several challenges that OECD countries are currently facing when planning and providing public funding of R&D sphere. These issues are analyzed within more general framework - increase of efficiency of public spending of R&D and Science, Technology and Innovation (STI) sector as a whole. The authors examine application of public R&D funding based on socio-economic classification (Frascati Manual 2015), optimal choice of forms and instruments of R&D public funding, which is linked with desired outputs and socio-economic outcomes, and methodologies of efficiency evaluation of public funding of R&D in OECD. Moreover, the authors draw the conclusion about marked extension of the list and variety of forms, methods and instruments of R&D public funding after 2007-08 global financial crisis. In addition to traditional institutional (block grants) and project financing, new form - Research Excellence Initiative (REI) - has evolved. It combines features of institutional core funding (long-termed, program format, etc.) with competitive organization and outcome orientation. It is especially efficient and effective when the focus is made on exceptional quality of research, interdisciplinary and multi-university studies. Integration of performance budgeting elements in institutional funding (e.g., performance contracts) is another noticeable trend in the evolution of public financing in OECD countries during the last decade. At the same time, the certain limits of project-based financing and application of competitive mechanisms in organization of R&D public funding became more evident, because of shorter terms and more risks associated with such projects. One more conclusion refers to wider application of holistic approach to efficiency evaluation of R&D public funding in OECD countries, when efficiency is evaluated at every stage of R&D process. Results of the research can be used in spending reviews in R&D or STI area as well as in recommendations for increasing efficiency of public governance of these areas.