A decade of warm hot intergalactic medium searches: Where do we stand and where do we go?

In this article, we first review the past decade of efforts in detecting the missing baryons in the warm hot intergalactic medium and summarize the current state of the art by updating the baryon census and physical state of the detected baryons in the local Universe. We then describe observational strategies that should enable a significant step forward in the next decade, while waiting for the step-up in quality offered by future missions. In particular, we design a multi-megasecond and multiple cycle XMM-Newton legacy' program (which we name the Ultimate Roaming Baryon Exploration, or URBE), aimed at securing detections of the peaks in the density distribution of the Universe of missing baryons over their entire predicted range of temperatures.