The representation of the atmospheric boundary layer is an important part of weather and climate models and impacts many applications such as air quality and wind energy. Over the years, the performance in modeling 2 m temperature and 10 m wind speed has improved but errors are still significant. This is in particular the case under clear skies and low wind-speed conditions at night as well as during winter in stably stratified conditions over land and ice. In this paper, we review these issues and provide an overview of the current understanding and model performance. Results from weather forecast and climate models are used to illustrate the state of the art, as well as findings and recommendations from three inter-comparison studies held within the "Global Energy and Water Exchanges (GEWEX)" Atmospheric Boundary Layer Study (GABLS). Within GABLS, the focus has been on the examination of the representation of the stable boundary layer and the diurnal cycle over land in clear sky conditions. For this purpose, single-column versions of weather and climate models have been compared with observations, research models and Large Eddy Simulations. The intercomparison cases are based on observations taken in the Arctic, Kansas and at Cabauw in the Netherlands. From these studies, we find that even for the non-cloudy boundary layer important parameterization challenges remain.