If the plans are still on schedule, Heathrow Airport is to begin the process of closing Terminal 3 and Terminal 4 from today.
(EDIT: the closure has been delayed, and the move will start on Thursday 16th April)
Remaining flights will be consolidated in Terminal 2 and Terminal 5.
The rough plan is for the Terminal 4 airlines to move into Terminal 5, alongside British Airways, whilst the Terminal 3 airlines will move into Terminal 2. Given all of the lounges and shops are closed, apart from a handful of restaurants, there will be minimal difference in terms of the travel experience.
This is not a big bang move, with everyone moving on the same day, so please check your terminal carefully if you are expecting to fly from Terminal 3 or Terminal 4 at any point soon.