Publication bias is a well-known threat to the validity of meta-analyses and, more broadly, the reproducibility of scientific findings. When policies and recommendations are predicated on an incomplete evidence base, it undermines the goals of evidence-based decision-making. Great strides have been made in the last 50 years to understand and address this problem, including calls for mandatory trial registration and the development of statistical methods to detect and correct for publication bias. We offer an historical account of seminal contributions by the evidence synthesis community, with an emphasis on the parallel development of graph-based and selection model approaches. We also draw attention to current innovations and opportunities for future methodological work.