Abstract: Horizontal convective rolls (HCRs) are defined as horizontal vortices that rotate in the opposite direction within the convective boundary layer. They are one of the common forms of shallow convection in the atmosphere. HCRs can cause strong turbulence and water vapor mixing in the boundary layer as well as exchanges of mass, momentum, and heat flux between the boundary layer and the free atmosphere. Meteorologists have conducted systematic research on structural characteristics, formation mechanisms, and impacts on the boundary layer of HCRs through field observation experiments, theoretical derivation, flume experiments, and numerical simulations. The results indicate that inflection-point instability and thermal instability are the main mechanisms for the formation of HCRs. The turbulent flux transport by HCRs can cause non-uniform distribution of flux in the horizontal direction of the boundary layer. The vertical motion, high specific humidity, and positive temperature anomalies in the ascending branch of the HCR provide favorable conditions for cold-flow snowstorm and deep convection. At present, large eddy simulation is the main numerical method for studying HCRs. However, the mechanisms by which HCRs trigger heavy snowfall and independently trigger deep convection are still unclear. It is proposed to accelerate the application of new remote sensing technology in field experiments and establish three-dimensional structural models for HCR studies. Cloud penetration experiments on cold flow snow processes should be conducted to explore the effects of HCR-related aerosols and flux transport on ice microphysical processes. Based on comparative analysis of structural characteristics of HCRs and environmental conditions that can trigger deep convection, a simple and efficient nowcasting model or operation procedures that can simulate deep convections triggered by HCRs should be developed with the aim to improve operational forecasting of catastrophic weathers caused by HCRs.