We propose, and formalize, a new framework for research synthesis of both evidence and influence, named ‘research weaving’. It summarizes and visualizes information content, history, and networks among a collection of diverse publication types on any given topic. Research weaving achieves this feat by combining the power of two methodologies: systematic mapping and bibliometrics. Systematic mapping provides a snapshot of the current state of knowledge, identifying areas needing more research attention and those ready for full synthesis (e.g., using meta-analysis). Bibliometrics enables researchers to see how pieces of evidence are connected, revealing the structure and the evolution of a field. We explain how to become a ‘research weaver’, and discuss how research weaving may change the landscape of research synthesis.