millis() rollover

I too have followed the millis() rollover thing for sometime now. I get how it was changed to a long, so the rollover was increased to 50+ days or so.

What I don't get is the several statements made in various postings that now a programs flow can operate OK through a roll-over? Can some explain this in simple terms, how the edge condition of roll-over can continue without blowing up if statements using it.

Typically one saves a copy of the millis() count as the 'current time' and that is used later when compared to a new millis() count to see if a specific time has elapsed or not. How does the roll-over effect that use of logic?

Lefty