Applications can be made from nationals of the EU as well as nationals of Iceland, Liechtenstein and Norway plus family members.
Depending on how long they have lived in the UK those eligible will be granted “settled status” or “pre-settled status.”
There have already been some technical hitches but applications are generally straightforward and free of charge.
You will see lots of relevant information in the link above but please contact Jenny Harvey on firstname.lastname@example.org if you have questions or would like assistance with an application. It may be sensible to ask for advice before making an application if you have lived in the UK for more than 5 years and if you are hoping to apply for British Citizenship. Settled status will not be backdated and you may need to wait a further year until you are able to apply to become British. If you “acquired” permanent residence under current EU rules you may already be able to apply.