Transmission of the coronavirus disease 2019 is still ongoing despite mass vaccination, lockdowns, and other drastic measures to control the pandemic. This is due partly to our lack of understanding on the multiphase flow mechanics that control droplet transport and viral transmission dynamics. Various models of droplet evaporation have been reported, yet there is still limited knowledge about the influence of physicochemical parameters on the transport of respiratory droplets carrying the severe acute respiratory syndrome coronavirus 2. Here we review the effects of initial droplet size, environmental conditions, virus mutation, and non-volatile components on droplet evaporation and dispersion, and on virus stability. We present experimental and computational methods to analyze droplet transport, and factors controlling transport and evaporation. Methods include thermal manikins, flow techniques, aerosol-generating techniques, nucleic acid-based assays, antibody-based assays, polymerase chain reaction, loop-mediated isothermal amplification, field-effect transistor-based assay, and discrete and gas-phase modeling. Controlling factors include environmental conditions, turbulence, ventilation, ambient temperature, relative humidity, droplet size distribution, non-volatile components, evaporation and mutation. Current results show that medium-sized droplets, e.g., 50 µm, are sensitive to relative humidity. Medium-sized droplets experience delayed evaporation at high relative humidity, and increase airborne lifetime and travel distance. By contrast, at low relative humidity, medium-sized droplets quickly shrink to droplet nuclei and follow the cough jet. Virus inactivation within a few hours generally occurs at temperatures above 40 °C, and the presence of viral particles in aerosols impedes droplet evaporation.