SN 2014J in M82 is the closest detected Type Ia supernova (SN Ia) in at least 28 years and perhaps in 410 years. Despite its small distance of 3.3 Mpc, SN 2014J is surprisingly faint, peaking at V = 10.6 mag, and assuming a typical SN Ia luminosity, we infer an observed visual extinction of A_V = 2.0 +/- 0.1 mag. But this picture, with R_V = 1.6 +/- 0.2, is too simple to account for all observations. We combine 10 epochs (spanning a month) of HST/STIS ultraviolet through near-infrared spectroscopy with HST/WFC3, KAIT, and FanCam photometry from the optical to the infrared and 9 epochs of high-resolution TRES spectroscopy to investigate the sources of extinction and reddening for SN 2014J. We argue that the wide range of observed properties for SN 2014J is caused by a combination of dust reddening, likely originating in the interstellar medium of M82, and scattering off circumstellar material. For this model, roughly half of the extinction is caused by reddening from typical dust (E(B-V ) = 0.45 mag and R_V = 2.6) and roughly half by scattering off LMC-like dust in the circumstellar environment of SN 2014J.