We present a multiwavelength study of the 90 brightest cluster galaxies (BCGs) in a sample of galaxy clusters selected via the Sunyaev Zel'dovich effect by the South Pole Telescope, utilizing data from various ground-and space-based facilities. We infer the star-formation rate (SFR) for the BCG in each cluster-based on the UV and IR continuum luminosity, as well as the [O II]λλ3726,3729 emission line luminosity in cases where spectroscopy is available-and find seven systems with SFR > 100 M e yr −1 . We find that the BCG SFR exceeds 10 M e yr −1 in 31 of 90 (34%) cases at 0.25<z<1.25, compared to ∼1%-5% at z∼0 from the literature. At z1, this fraction increases to 92 31 6 -+ %, implying a steady decrease in the BCG SFR over the past ∼9 Gyr. At low-z, we find that the specific SFR in BCGs is declining more slowly with time than for field or cluster galaxies, which is most likely due to the replenishing fuel from the cooling ICM in relaxed, cool core clusters. At z0.6, the correlation between the cluster central entropy and BCG star formation-which is well established at z∼0-is not present. Instead, we find that the most star-forming BCGs at high-z are found in the cores of dynamically unrelaxed clusters. We use data from the Hubble Space Telescope to investigate the rest-frame near-UV morphology of a subsample of the most star-forming BCGs, and find complex, highly asymmetric UV morphologies on scales as large as ∼50-60 kpc. The high fraction of star-forming BCGs hosted in unrelaxed, non-cool core clusters at early times suggests that the dominant mode of fueling star formation in BCGs may have recently transitioned from galaxygalaxy interactions to ICM cooling.