The elucidation of a compound's Mechanism of Action (MoA) is a challenging task in the drug discovery process, but it is important in order to rationalise phenotypic findings and to anticipate potential side-effects. Bioinformatic approaches, advances in machine learning techniques and the increasing deposition of high-throughput data in public databases have significantly contributed to recent advances in the field, but it is not straightforward to decide which data and methods are most suitable to use in a given case. In this review, we focus on these methods and data and their applications in generating MoA hypotheses for subsequent experimental validation. We discuss compound-specific data such as -omics, cell morphology and bioactivity data, as well as commonly used supplementary prior knowledge such as network and pathway data, and provide information on databases where this data can be accessed. In terms of methodologies, we discuss both well-established methods (connectivity mapping, pathway enrichment) as well as more developing methods (neural networks and multi-omics integration). Finally, we review case studies where the MoA of a compound was successfully suggested from computational analysis by incorporating multiple data modalities and/or methodologies. Our aim for this review is to provide researchers with insights into the benefits and drawbacks of both the data and methods in terms of level of understanding, biases and interpretation - and to highlight future avenues of investigation which we foresee will improve the field of MoA elucidation, including greater public access to -omics data and methodologies which are capable of data integration.