My car started this morning as usual but when I put in reverse nothing happened, it didn't shift. The same thing occurred when I put it in drive, it didn't go. When I stepped on the accelerator the engine revved but no movement. Is it the transmission? And if yes what's wrong?

If you haven't dropped and cleaned the pan, changed the filter, and replaced the transmission fluid every 30,000 miles, you are likely looking at a rebuild. The clutch pack is likely shot.