Abstract. During the 1950s and 1960s, when intensive investigations on atmospheric moist convection were launched, two possibilities were identified for the basic element of moist convection: bubble and plume. The present paper reviews the investigations of this period, and suggests how the mass-flux convection parameterization formulation emerged from these early investigations. The choice of the steady-plume model as a key ingredient of the mass-flux formulation is especially carefully discussed. Some historical lessons are suggested, especially in the light of the current trend of more emphasis on the bubble dynamics as elucidated by high-resolution numerical modeling and laboratory experiments.