Aerosol particles in the atmosphere profoundly influence public health and climate. Ultrafine particles enter the body through the lungs and can translocate to essentially all organs, and they represent a major yet poorly understood health risk. Human activities have considerably increased aerosols and cloudiness since preindustrial times, but they remain persistently uncertain and underrepresented in global climate models. Here we present a synthesis of the current understanding of atmospheric new particle formation derived from laboratory measurements at the CERN CLOUD chamber. Whereas the importance of sulfuric acid has long been recognized, condensable vapours such as highly oxygenated organics and iodine oxoacids also play key roles, together with stabilizers such as ammonia, amines and ions from galactic cosmic rays. We discuss how insights from CLOUD experiments are helping to interpret new particle formation in different atmospheric environments, and to provide a mechanistic foundation for air quality and climate models.