Research funding systems fundamentally influence how science operates. This paper aims to analyze the allocation of competitive research funding from different perspectives: How reliable are decision processes for funding? What are the economic costs of competitive funding? How does competition for funds affect doing risky research? How do competitive funding environments affect scientists themselves, and which ethical issues must be considered? We attempt to identify gaps in our knowledge of research funding systems; we propose recommendations for policymakers and funding agencies, including empirical experiments of decision processes and the collection of data on these processes. With our recommendations, we hope to contribute to developing improved ways of organizing research funding.