The present paper reviews our latest, and brings several new, results on charging of dust grains of various materials and sizes. Charging processes of dust in space and their influence on the dust dynamics are analyzed in laboratory simulations of secondary emission, field ion and electron emissions, and dust sputtering. Single micrometre-sized grains and grain clusters are stored in a hyperbolic quadrupole field under ultra-high vacuum conditions for long time periods. The charge state of the grain and its evolution are recorded while the grain is exposed to ion or electron beams of various energies and fluxes. The influence of the secondary electron emission on the charge state is measured and compared with a computer model. Limitations on the grain charge by the field electron and ion emission are considered next. The measurements allow analyzing field emission from conductive and dielectric grains. The existence of long-lived surface states on insulating materials, which are probably responsible for the anomalous behavior of field electron emission and the low threshold of the field ion emission, is indicated. The observation of sputtering by energetic ions showing a surprising anisotropic erosion of a conductive grain is analyzed. The sputtering and the field ion emission are discussed as possible sources of the so-called pick-up ions.