The verb se moquer is used in two recent videos, in two slightly different senses:

Et il n'est pas le seul à se moquer.

And he's not the only one making fun.

Caption 40, d'Art d'Art - "Impression, soleil levant" - Monet

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Non mais tu te moques de moi?

No but are you kidding me?

Caption 61, Le Jour où tout a basculé - Ma fille et mon mari se sont fait berner

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BANNER PLACEHOLDER

Se moquer means to make or poke fun, or to kid. If it takes an object, as in the second example, you have to add de after it (to make fun of someone). It's cognate with "to mock" in English, and can also have that sense, depending on context: 

Se moquer gentiment de personnages célèbres est très courant

Gently mocking famous people is very common

pendant la période de carnaval.

during the carnival period.

Caption 20, Le saviez-vous? - Le carnaval en France

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But se moquer has another meaning that isn't quite as obvious. It's the verb you use when you don't care about something, or more precisely, when you couldn't care less:

Je me moque des règles. 

I couldn't care less about the rules.

In more informal speech, se ficher is often used instead of se moquer in most of its senses:

On se fiche de nous ou quoi?

Are you kidding us or what?

Caption 5, Actus Quartier - Devant la SNCF

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Je me fiche des règles.

I couldn't care less about the rules.

Another way of saying "to make/poke fun" is taquiner (to tease):

Ne taquine pas ta sœur.

Don't tease your sister.

There are a few other verbs for "to kid" in French. If you want to say "I'm kidding" or "just kidding," use plaisanter or rigoler:

Je plaisante, pas du tout.

I'm kidding, not at all.

Caption 22, Elisa et Mashal - Mon chien Roméo

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Je ne ferai pas l'idiote. Non, je rigole.

I will not act like an idiot. No, I'm kidding.

Caption 52, Margaux et Manon - Conjugaison du verbe faire

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Rigoler is an informal synonym of rire (to laugh). So you can think of je rigole as "I'm just having a laugh." Plaisanter, the verb form of une plaisanterie (a joke), means "to joke" or "joke around." So je plaisante is more along the lines of "I'm just joking around."

If you want to say "you're kidding," as an exclamation, you can say, Tu plaisantes! Or, you can even just say, Tu parles! (literally, "You're talking!")

Tu parles. Impôts?

You're kidding. Taxes?

Caption 37, Patricia - Pas de crédit dans le monde des clones

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And for the phrase "no kidding," you can use the phrase sans blague (no joke). For more on that and other joke-related expressions, see our lesson Telling Jokes in French.