Universities Scotland director Alastair Sim warned further outbreaks among students remain likely.
Students can return home on a 'long-term basis' but not for short overnight stays, new guidance says.
The education secretary said getting students home to their families at Christmas is 'at the heart of our thinking'.
Nicola Sturgeon addressed students after they were banned from pubs and socialising outside their households.
UCU Scotland accuses principals of 'blaming students' for Covid outbreaks after 'encouraging' them back to campuses.
Students living in flats and halls can't visit their parents indoors as they are considered separate households.
A review will be conducted by the Scottish Funding Council into how higher education can be funded post-pandemic.
A group of medical students have launched a one-stop shop support scheme for NHS workers during the coronavirus pandemic.
The University and College Union said its members at 13 Scottish universities will take part in 14 days of strike action.