 This review consists of four distinct parts. First, we look at the term “reproducibility” and related terms like “repeatability” and “replication”, presenting some definitions and conceptual discussion about the epistemic function of different types of replication studies. Second, we describe the meta-science research that has established and characterised the reproducibility crisis, including large scale replication projects and surveys of questionable research practices in various scientific communities. Third, we look at attempts to address epistemological questions about the limitations of replication, and what value it holds for scientific inquiry and the accumulation of knowledge. The fourth and final part describes some of the many initiatives the open science reform movement has proposed (and in many cases implemented) to improve reproducibility in science. In addition, we reflect there on the values and norms which those reforms embody, noting their relevance to the debate about the role of values in the philosophy of science.