A long-standing question in infectious disease dynamics is the role of transmission heterogeneities, particularly those driven by demography, behavior and interventions. Here we characterize transmission risk between 1,178 SARS-CoV-2 infected individuals and their 15,648 close contacts based on detailed contact tracing data from Hunan, China. We find that 80% of secondary transmissions can be traced back to 14% of SARS-CoV-2 infections, indicating substantial transmission heterogeneities. Regression analysis suggests a marked gradient of transmission risk scales positively with the duration of exposure and the closeness of social interactions, after adjusted for demographic and clinical factors. Population-level physical distancing measures confine transmission to families and households; while case isolation and contact quarantine reduce transmission in all settings. Adjusted for interventions, the reconstructed infectiousness profile of a typical SARS-CoV-2 infection peaks just before symptom presentation, with ~50% of transmission occurring in the pre-symptomatic phase. Modelling results indicate that achieving SARS-CoV-2 control would require the synergistic efforts of case isolation, contact quarantine, and population-level physical distancing measures, owing to the particular transmission kinetics of this virus.