I present the current status of the phenomenology for the anomalous magnetic moment of the muon, g_\mu - 2, which presently constitutes one of the most important tensions between experiment and the Standard Model. This is followed by a brief introduction to lattice QCD and a discussion of RBC/UKQCD's programme for the computation from first principles of this important quantity. I focus in particular on our recent successes in computing the strange and disconnected contributions, presenting some results from our recent papers.