Turbulent buoyant plumes represent one of the fundamental convective elements, being produced by maintained sources of heat and/or momentum. They occur in natural systems such as the atmosphere and oceans, and they are considered the principle mechanism responsible for the vertical transport of heat and moisture in the atmosphere. The theoretical formulation of atmospheric convection, on which the majority of the current climate models are based, relies on the assumption that the atmospheric convective elements are entraining jets. Moreover, since the convection is the principal mechanism responsible for the water cycle in the atmosphere, which controls the radiation balance of the earth, the representation of atmospheric convection is crucial in order to understand the climate and to be able to make climate projections. In this presentation, this aspects will be discussed, together with a brief discussion on the present research challenging we are facing in theoretical climatology.