Facing was part of the original Nolaria combat system and thus was part of the "flavor" of the game.
The DMG describes optional rules for facing on p.252. At the end of each combat turn, a creature may adjust it's facing. Facing may also be changed as a reaction to another creature's move.
Facing arcs on a square grid look like this:
Shields provide plus AC on the front arc and the shield arm side.
Attacks may be done on front or side arcs.
The creature cannot see anything in it's rear arc and cannot attack in that direction without changing facing.
Flanking applies only to front and side arcs.