The formation of ice particles in the Earth's atmosphere strongly affects the properties of clouds and their impact on climate. Despite the importance of ice formation in determining the properties of clouds, the Intergovernmental Panel on Climate Change (IPCC, 2007) was unable to assess the impact of atmospheric ice formation in their most recent report because our basic knowledge is insufficient. Part of the problem is the paucity of quantitative information on the ability of various atmospheric aerosol species to initiate ice formation. Here we review and assess the existing quantitative knowledge of ice nucleation by particles immersed within supercooled water droplets. We introduce aerosol species which have been identified in the past as potentially important ice nuclei and address their ice-nucleating ability when immersed in a supercooled droplet. We focus on mineral dusts, biological species (pollen, bacteria, fungal spores and plankton), carbonaceous combustion products and volcanic ash. In order to make a quantitative comparison we first introduce several ways of describing ice nucleation and then summarise the existing information according to the time-independent (singular) approximation. Using this approximation in combination with typical atmospheric loadings, we estimate the importance of ice nucleation by different aerosol types. According to these estimates we find that ice nucleation below about -15 °C is dominated by soot and mineral dusts. Above this temperature the only materials known to nucleate ice are biological, with quantitative data for other materials absent from the literature. We conclude with a summary of the challenges our community faces.