The Frightened condition gives the following penalty:
A frightened creature has disadvantage on Ability Checks and Attack rolls while the source of its fear is within line of sight.
Many monsters have sight-based abilities that allow the target to avoid the effect by averting its eyes:
Basilisk's Petrifying Gaze: A creature that isn't surprised can avert its eyes to avoid the saving throw at the start of its turn. If it does so, it can't see the basilisk until the start of its next turn, when it can avert its eyes again.
Medusa's Petrifying Gaze: Unless surprised, a creature can avert its eyes to avoid the saving throw at the start of its turn. If the creature does so, it can't see the medusa until the start of its next turn, when it can avert its eyes again.
Can a creature "avert its eyes" away from any creature? Or can you only avert your eyes from a creatures if it says so in the creature's statblock?
When suffering from the Frightened condition, adverting your eyes from the source of the fear would be very useful as it would remove the source from your line of sight, effectively negating the disadvantage to attack rolls and ability checks.