The INTEGRAL mission has played a major role in blazar science, thanks to its sensitive coverage of a spectral region (3-100 keV) that is critical for this type of sources, to its flexibility of scheduling and to the large field of view of its cameras. A number of flat-spectrum radio quasars (up to z ~ 3) and BL Lac objects were observed by INTEGRAL together with facilities at all wavelengths. These results have advanced our knowledge of blazars from a physical and cosmological point of view. This paper reviews some of these outcomes, with particular reference to the INTEGRAL program for blazars in outburst as targets of opportunity, with a perspective into a future of multi-messenger astronomy