We present the results of X-ray and near-IR observations of the anomalous X-ray pulsar 1E 1048.1-5937, believed to be a magnetar. This AXP underwent a period of extreme variability during 2001-2004, but subsequently entered an extended and unexpected quiescence in 2004-2006, during which we monitored it with RXTE, CXO, and HST. Its timing properties were stable for >3 years throughout the quiescent period. 1E 1048.1-5937 again went into outburst in March 2007, which saw a factor of >7 total X-ray flux increase which was anti-correlated with a pulsed fraction decrease, and correlated with spectral hardening, among other effects. The near-IR counterpart also brightened following the 2007 event. We discuss our findings in the context of the magnetar and other models.