Ideally decisions regarding medical treatments would be informed by the totality of the available evidence. The best evidence we currently have is in published natural language articles describing the conduct and results of clinical trials. Because these are unstructured, it is difficult for domain experts (e.g., physicians) to sort through and appraise the evidence pertaining to a given clinical question. Natural language technologies have the potential to improve access to the evidence via semi-automated processing of the biomedical literature. In this brief paper I highlight work on developing tasks, corpora, and models to support semi-automated evidence retrieval and extraction. The aim is to design models that can consume articles describing clinical trials and automatically extract from these key clinical variables and findings, and estimate their reliability. Completely automating `machine reading' of evidence remains a distant aim given current technologies; the more immediate hope is to use such technologies to help domain experts access and make sense of unstructured biomedical evidence more efficiently, with the ultimate aim of improving patient care. Aside from their practical importance, these tasks pose core NLP challenges that directly motivate methodological innovation.