Numerical Weather Prediction (NWP) in complex terrain is a challeging task. The experience collected with the COSMO model - a limited area NWP non-hydrostatic model operated by MeteoSwiss in the Alpine region - indicates that several meteorological aspects mainly at local scale are still not well reproduced. The present study focuses on some challenging aspects of NWP at high resolution in complex terrain. This work explores the topographic effects on radiation, tests the performance of the turbulence scheme in a semi-idealized setup using the single column version of COSMO at high vertical resolution, evaluates its ability to reproduce a realistic diurnal cycle and analyses the deficiencies of the COSMO 2 m temperature diagnostics in the alpine region.