Reproducible computational research (RCR) is the keystone of the scientific method for in silico analyses, packaging the transformation of raw data to published results. In addition to its role in research integrity, improving the reproducibility of scientific studies can accelerate evaluation and reuse. This potential and wide support for the FAIR principles have motivated interest in metadata standards supporting reproducibility. Metadata provide context and provenance to raw data and methods and are essential to both discovery and validation. Despite this shared connection with scientific data, few studies have explicitly described how metadata enable reproducible computational research. This review employs a functional content analysis to identify metadata standards that support reproducibility across an analytic stack consisting of input data, tools, notebooks, pipelines, and publications. Our review provides background context, explores gaps, and discovers component trends of embeddedness and methodology weight from which we derive recommendations for future work.