Substantial uncertainties exist in the current knowledge of aerosol-cloud-precipitation relationships and stem from the complicated interactions among the atmospheric constituents. We use a straightforward statistical method, the regression analysis technique, to examine the aerosol-cloud-precipitation relationships from satellite observational data sets, including the aqua moderate resolution imaging spectroradiometer (MODIS) aerosol and cloud products and the tropical rainfall measuring mission (TRMM) precipitation rate. Furthermore, the conventional MODIS aerosol product is combined with the Deep Blue algorithm product to reconstruct a complete global map of aerosol optical depth. Numerical simulations using the latest version of the community earth system model (CESM) are also carried out. Globally, distinct statistically significant relationships between aerosol optical depth, cloud fraction, and precipitation rate are obtained over both land and ocean. Signals agreeing with the first and second indirect effects of aerosols are detected, but other factors are likely contributors. The modeling results are found to generally agree with satellite observations, but the model usually overestimates the aerosol-cloud-precipitation relationship. An increasing trend in cloud fraction with the increase of aerosol optical depth (AOD) over ocean regions is found in the observations, while the reverse is true in the model simulation. It is mostly consistent that the model and observation both show a negative relationship between AOD and precipitation rate over land and a positive relationship over ocean.