Dust emission in the diffuse interstellar medium from far-infrared to millimeter: new constraints from WMAP

This paper proposes a short review on our knowledge on the dust emission in the diffuse sky from far-IR to the mm wavelength. The current understanding is based mainly on the analysis of the COBE data combined with several templates of gas tracers (HI and Halpha). In the millimeter, emphasis is given to the new WMAP results on the so-called ``anomalous microwave emission’'.