The year 2015 was special for climate scientists, particularly for the El Niño Southern Oscillation (ENSO) research community, as a major El Niño finally materialized after a long pause since the 1997/1998 extreme El Niño. It was scientifically exciting since, due to the short observational record, our knowledge of an extreme El Niño has been based only on the 1982/1983 and 1997/1998 events. The 2015/2016 El Niño was marked by many environmental disasters that are consistent with what is expected for an extreme El Niño. Considering the dramatic impacts of extreme El Niño, and the risk of a potential increase in frequency of ENSO extremes under greenhouse warming, it is timely to evaluate how the recent event fits into our understanding of ENSO extremes. Here we provide a review of ENSO, its nature and dynamics, and through analysis of various observed key variables, we outline the processes that characterize its extremes. The 2015/2016 El Niño brings a useful perspective into the state of understanding of these events and highlights areas for future research. While the 2015/2016 El Niño is characteristically distinct from the 1982/1983 and 1997/1998 events, it still can be considered as the first extreme El Niño of the 21st century. Its extremity can be attributed in part to unusually warm condition in 2014 and to long‐term background warming. In effect, this study provides a list of physically meaningful indices that are straightforward to compute for identifying and tracking extreme ENSO events in observations and climate models. Plain Language Summary The El Niño Southern Oscillation (ENSO) continues to boast its prominence as Earth's strongest source of year‐to‐year climate variability with the appearance of a remarkable El Niño event in 2015–2016. The 2015/2016 El Niño was indeed a strong event with dramatic impact on a global scale. However, it exhibited distinct characteristics from those of past extreme El Niños in modern instrumental record. This challenges our previous understanding of an extreme El Niño which is important for ENSO prediction, monitoring, and future projections. The 2015/2016 El Niño has diversified the small sample of ENSO events in our short instrumental record. It has facilitated important discussions on our progress in understanding the nature of ENSO and its extremes, how they respond to greenhouse warming, and what the climate science community should do next in their quest to fully grasp the complexity of ENSO behavior. These are covered in this review paper which establishes the 2015/2016 El Niño as the first extreme El Niño of the 21st century. Key Points The 2015/2016 El Niño is the first extreme El Niño of the 21st century The 2015/2016 El Niño contributes to a better understanding of ENSO extremes Multiple simple indices can be used to monitor and identify ENSO extremes