Several of the current and next-generation cosmic microwave background(CMB) experiments have polarimetric capability, promising to add tothe finesse of precision cosmology. One of the contaminating Galacticforegrounds is thermal emission by dust. Since optical interstellarpolarization is commonly seen, from differential extinction by alignedaspherical dust particles, it is expected that thermal emission fromthese grains will be polarized. Indeed, in the Galactic plane and indark (molecular) clouds, dust emission in the infrared andsubmillimetre has been measured to be polarized. It seems likely thatthe faint diffuse cirrus emission, of more relevance to CMBexperiments, will be polarized too. We discuss how well the amount ofpolarization of this component can be predicted, making use of what isknown about optical (and infrared and ultraviolet) interstellarpolarization and extinction. Some constraints on the alignment of thecarrier of the dust-correlated anomalous microwave emission can bemade as well.