Cumulus clouds are pervasive on earth, and play important roles in the transfer of energy through the atmosphere. Under certain conditions, shallow, nonprecipitating cumuli may grow vertically to occupy a significant depth of the troposphere, and subsequently may evolve into convective storms. The qualifier “convective” implies that the storms have vertical accelerations that are driven primarily, though not exclusively, by buoyancy over a deep layer. Such buoyancy in the atmosphere arises from local density variations relative to some base state density; the base state is typically idealized as a horizontal average over a large area, which is also considered the environment. Quantifications of atmospheric buoyancy are typically expressed in terms of temperature and humidity, and allow for an assessment of the likelihood that convective clouds will form or initiate. Convection initiation is intimately linked to existence of a mechanism by which air is vertically lifted to realize this buoyancy and thus accelerations. Weather fronts and orography are the canonical lifting mechanisms. As modulated by an ambient or environmental distribution of temperature, humidity, and wind, weather fronts also facilitate the transition of convective clouds into storms with locally heavy rain, lightning, and other possible hazards. For example, in an environment characterized by winds that are weak and change little with distance above the ground, the storms tend to be short lived and benign. The structure of the vertical drafts and other internal storm processes under weak wind shear—i.e., a small change in the horizontal wind over some vertical distance—are distinct relative to those when the environmental wind shear is strong. In particular, strong wind shear in combination with large buoyancy favors the development of squall lines and supercells, both of which are highly coherent storm types. Besides having durations that may exceed a few hours, both of these storm types tend to be particularly hazardous: squall lines are most apt to generate swaths of damaging “straight-line” winds, and supercells spawn the most intense tornadoes and are responsible for the largest hail. Methods used to predict convective-storm hazards capitalize on this knowledge of storm formation and development.