Atmospheric aerosol particles serve as condensation nuclei for the formation of both, cloud droplets and atmospheric ice particles. As a result, they exert a substantial influence on the microphysical properties of water and ice clouds, which in turn affect the processes that lead to the formation of rain, snow, hail, and other forms of precipitation. In recent years, considerable progress has been made in understanding the chemical composition of aerosols, their microphysical properties, and the factors that enable them to act as cloud condensation nuclei (CCN) and ice nuclei (IN). The first part of this review article will focus on the nature and sources of CCN and IN. We discuss the fundamentals of the cloud droplet and ice nucleation processes, and the role that the chemical composition and particle size play in this process. We show that, in many instances, the influence of chemical composition can be represented by a simple parameterization, which leaves particle size as the main variable controlling CCN efficiency. Aerosol particles are produced either directly by anthropogenic and natural sources (dust, sea salt, soot, biological particles, etc.), or they are formed in the atmosphere by condensation of low-volatility compounds (e.g., sulfuric acid or oxidized organic compounds). We discuss the magnitude of these sources, and the CCN and IN characteristics of the particles they produce. In contrast to previous assessments, which focused on the aerosol mass, we are emphasizing the number of particles being produced, as this is the key variable in cloud microphysics. Large uncertainties still exist for many aerosol sources, e.g., the submicron part of the seaspray aerosol, the particles produced by the biosphere, and the secondary organic aerosol. We conclude with a discussion on what particle concentrations may have been in the pristine atmosphere, before the onset on anthropogenic pollution. Model calculations and observations in remote continental regions consistently suggest that CCN concentrations over the pristine continents were similar to those now prevailing over the remote oceans, suggesting that human activities have modified cloud microphysics more than what is reflected in conventional wisdom. The second part of this review will address the effects of changing CCN and IN abundances on precipitation processes, the water cycle, and climate.