We summarize and discuss critically the various procedures used for decisions in evaluating and funding scientific research in view of the goal of obtaining the best research with a given funding volume. Merits, difficulties, and problems in some procedures are outlined. We identify a number of myths appearing frequently in the process of research evaluation. We indicate some similarities in deciding on funding research projects, making appointments to academic and leading research positions and selecting prize winners for high prizes for scientists. Challenges, risks and opportunities in research and its funding are identified.