up
out
on
for
apart, off, down
100

to end your relationship

to break up or to split up with someone

We decided to break up when he moved to Europe.

We were constantly arguing, so we had to split up.

100

to date someone 

to go out with someone

I have been going out with Harry for 3 months now.

100

to see someone romantically when you already have a partner

to cheat on someone

He promised he would never cheat on me.

100

to fall in love with someone

to fall for someone 

She fell for him the moment she met him.

100

to slowly lose your sense of connection

to drift apart

Without spending time or energy on their relationship, they slowly drifted apart

200

to forgive each other after an argument 

to make up 

We were arguing about something silly, so decided to make up.

200

to kiss passionately

to make out 

She doesn't want to make out in public. 

200

to let someone believe you are romantically interested in them, but you are not

to lead someone on

George really likes you, you shouldn't lead him on.

200

to accept something even though it is not exactly what you want

to settle for 

Don't settle for him; you could do so much better.

200

to like each other and get along right away

to hit it off

Wow, they really hit if off! They got along as soon as they met. 

300

to have a fight and not see each other

to fall out 

We fell out after he insulted my mother. 

Also used as a noun: We had a falling out. 

300

to form a long term, stable relationship with someone 

to settle down with someone

They are going to settle down with each other in her hometown.