At the end of "Tango," new on Yabla this week, Mélanie Laurent sings:
Parce qu'au fond tu l'aimes bien, elle te manquerait je crois
Because deep down you really love her, you would miss her, I think
Caption 52, Mélanie Laurent - "Circus" & "Tango"Play Caption
When you're talking about missing someone in French, manquer is the verb to use. However, in this context, manquer actually means "to be missing" rather than "to miss." Though elle te manquerait might appear to mean "she would miss you" upon first glance, its literal translation is actually "she would be missing from you," which is just another (perhaps more romantic) way of saying "you would miss her." So when talking to someone close to you whom you haven't seen in a while, make sure to say tu me manques ("I miss you," literally "you're missing from me") rather than je te manque ("you miss me," literally "I'm missing from you").
On the other hand, manquer does mean "to miss" when you're talking about missing something in the sense of not being there for it. In this context it's synonymous with the verb rater:
J'ai manqué [or raté] le bus.
I missed the bus.
The expression "manquer de + infinitive" (or just "manquer + infinitive") means "to nearly do something." "Faillir + infinitive" has the same meaning:
Il a manqué d'être tué [or: Il a failli être tué].
He was nearly killed.
But in the negative, this expression more often means "to not forget to do something":
Ne manquez pas de vous arrêter au numéro treize de l'avenue Junot.
Don't forget to stop at number thirteen Avenue Junot.
Caption 12, Voyage dans Paris - Butte MontmartrePlay Caption
Another common meaning of manquer is "to lack," usually in the expression "manquer de + noun":
L'hôpital manque de moyens, comme toutes nos formations sanitaires, hein?
The hospital lacks resources, like all our medical facilities, huh?Play Caption
In fact, the noun form of manquer, un manque, specifically means "a lack":
J'ai compris qu'il y avait un manque énorme au niveau, euh, alimentaire.
I saw that there was an enormous lack at the, uh, alimentary level.
Caption 7, Alsace 20 - Mangez bien, mangez alsacien!Play Caption
Finally, manquer is also used in the impersonal expression "il manque + noun" ("x is missing"):
Il ne manque plus que l'argent nécessaire.
All that's missing is the necessary money.Play Caption