Wildfires can be divided into two types, flaming or smouldering, depending on the dominant combustion processes. Both types are present in most wildfires, and despite being fundamentally different in chemical and physical terms, one transitions to the other. Traditionally, science has focused on flames, while smouldering is often misinterpreted. But smouldering wildfires are emerging as a global concern because they cause extensive air pollution, emit very large amounts of carbon, are difficult to detect and suppress, and could accelerate climate change. Central to the topic are smouldering peat fires that lead to the largest fires on Earth. Smouldering also dominates the residual burning after flames have died out and firebrand ignition. Finally, smouldering is an important part of Arctic wildfires, which are increasing in frequency. Here, we present a scientific overview of smouldering wildfires, the associated environmental and health issues, including climate change, and the challenges in prevention and mitigation.