In 5e AoO only activates (unless you have a particular ability that says otherwise) when an enemy flees or passes by (i.e leaves your reach).
Some feats allow you to use your AoO if an enemy casts a spell or come to you (some like warcaster allows you to use a spell to AoO)
The other usual reactions will be used if you receive damage, if you receive elemental damage, if an enemy casts a spell, if someone makes an attack against you or if you are in free falling.
The reactions are more simple in 5e: basically a way to reduce damage, evade the attack, nullify the spell or fall or retaliate against the attacker.
That always occurs in the enemy turn. You only have one reaction per turn (unless you have an ability that says otherwise) With this premises, you can guess that the tactical options that allows are complex and some reactions require more fine-tuning than the one provided by an on-off button; if possible.
