In the past 5 years, advances in anion-conductive membranes have opened the door for the development of advanced anion-exchange membrane fuel cells (AEMFCs) as the next generation of affordable fuel cells. Several recent works have shown that AEMFCs currently achieve nearly identical beginning-of-life performance as state-of-the-art proton exchange membrane fuel cells. However, until now, these high AEMFC performances have been reached with platinum-group metal (PGM)-based anode and cathode catalysts. In order to fulfill the potential of AEMFCs, such catalysts should in the near future be free of PGMs and, eventually, free of critical raw materials. Although great progress has been achieved in the development of PGM-free catalysts for the oxygen reduction reaction in basic media, significantly less attention has been paid to the catalysis of the hydrogen oxidation reaction (HOR). The much lower HOR activity of Pt in basic media compared with that in acid was itself revealed only relatively recently. While several PGM-based composite materials have shown improved HOR activity in basic media, the HOR kinetics remains slower than necessary for an ideal nonpolarizable electrode. In addition, attempts to move away from PGMs have hitherto resulted in high anode overpotentials, significantly reducing the performance of PGM-free AEMFCs. This would be a major barrier for the large-scale deployment of this technology once the other technological hurdles (e.g., membrane stability) have been overcome. A fundamental understanding of the HOR mechanism in basic media and of the main energy barriers needs to be firmly established to overcome this challenge. This review presents the current understanding of the HOR electrocatalysis in basic media and critically discusses the most recent material approaches. Promising future research directions in the development of the HOR electrocatalysts for alkaline electrolytes are also outlined.