We have been observing a number of blazars with the Very Long Baseline Array in concert with monitoring at other wavebands, including X-rays and gamma-rays. Observations over several years demonstrate that there is an intimate connection between the ejection of apparent superluminal knots in the relativistic jets and X-ray or gamma-ray flares in blazars. The high-energy emission tends to be simultaneous with or even to follow the radio event, which leads to the surprising conclusion that all the highly variable emission comes from the radio-emitting part of the jet, which lies at distances of parsecs from the supermassive black hole. In the radio galaxy 3C 120, an X-ray dip precedes the ejection of each superluminal feature, similar to what is seen in the "microquasar" GRS 1915+105 in our Galaxy.