The authors thank B. Lott, L. Baldini, P. Bruel, S. Digel, J. Finke, D. Gasparini, N. Omodei, J. S. Perkins and A. Reimer for discussions that have significantly improved this publication. We acknowledge support and partial funding by the Deutsche Forschungsgemeinschaft grant WI 1860-10/1 (TANAMI) and GRK 1147, Deutsches Zentrum für Luft- und Raumfahrt grant 50 OR 1311/50 OR 1303/50 OR 1401, the German Ministry for Education and Research (BMBF) grants 05A11WEA and 05A14WE3, the Helmholtz Alliance for Astroparticle Physics (HAP), the Spanish MINECO project AYA2012-38491-C02-01, the Generalitat Valenciana project PROMETEOII/2014/057, the COST MP0905 action ‘Black Holes in a Violent Universe’ and NASA through Fermi Guest Investigator grants NNH09ZDA001N, NNH10ZDA001N, NNH12ZDA001N and NNH13ZDA001N. This study made use of data collected by the Australian Long Baseline Array (LBA) and the AuScope initiative. The LBA is part of the Australia Telescope National Facility, which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. AuScope Ltd is funded under the National Collaborative Research Infrastructure Strategy (NCRIS), an Australian Commonwealth Government Programme. This paper made use of data from the ALMA calibrator database: https://almascience.eso.org/alma-data/calibrator-catalogue. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. This paper also made use of up-to-date SMARTS optical/near-infrared light curves that are available at www.astro.yale.edu/smarts/glast/home.php. The Fermi–LAT Collaboration acknowledges support for LAT development, operation and data analysis from NASA and DOE (United States), CEA/Irfu and IN2P3/CNRS (France), ASI and INFN (Italy), MEXT, KEK, and JAXA (Japan), and the K. A. Wallenberg Foundation, the Swedish Research Council and the National Space Board (Sweden). Science analysis support in the operations phase from INAF (Italy) and CNES (France) is also gratefully acknowledged. We thank J. E. Davis and T. Johnson for the development of the slxfig module and the SED scripts that have been used to prepare the figures in this work.