I’ve had to do quite a lot of deviation over the years, some of it authorised. You could be on a track system, airway or random route and each has their own subtleties - have a look through your OM C and country regulations for the particular chunk of airspace.
If there’s a nasty bit of weather which you think would be unsafe to fly through, then you’re going to go around it. Next thing is to tell those affected by your decision and if you can’t get through to ATC then broadcasts on 121.5 and any chat frequencies should be received by anyone near enough to be a problem, a bit like the IFBP in parts of Africa. TCAS is not a replacement for proper separation but it sure helps; putting all the lights on wouldn’t be a bad idea, either.