In recent years, a large amount of data has been collected with the aim to quantify the day- and nighttime astronomical observing conditions at Dome C. The available data show that the precipitable water vapor is below 0.75 mm in general, thus offering very good conditions for sub-mm observations. The extremely low temperatures of the atmosphere cause a very low background in the thermal infrared, which leads to significant savings in the time required to carry out large observing programmes. The absence of strong turbulence in the upper atmosphere results in a low scintillation and poses favorable conditions for photometric programmes. The free atmosphere seeing is of the order of $0\farcs 36$, but optical observations are impaired by the occurrence of a very strong turbulent boundary layer which reaches up to median altitudes of some 23 m in winter and up to some 400 m in summer. Detailed measurements of the vertical and temporal variation of the various parameters are now needed, in order to draw robust conclusions about short- and long-term stabilities and trends, and to constrain the specifications of future instruments that are eventually being deployed at Dome C.