If you have any worries, concerns, or problems in a French-speaking country, souci is the word to use to express your predicament. In the first two senses ("worry" and "concern"), it's synonymous with inquiétude: 

BANNER PLACEHOLDER

Ne te fais pas de souci. Fais-moi confiance!

Don't worry. Trust me!

Caption 6, Il était une fois... l’Homme - 6. Le siècle de Périclès - Part 4

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Alors, le souci, quand elles en font deux, c'est que si elles sont pas très bonnes productrices de lait...

So the concern, when they have two, is that if they are not very good producers of milk...

Caption 4, Ferme de la Croix de Pierre - Les chèvres

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Pas d'inquiétude. De nos jours, le pont est protégé d'un grillage.

Not to worry. Nowadays, the bridge is protected by a wire fence.

Caption 29, De nouvelles découvertes avec Marion - Le parc des Buttes Chaumont

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Souci and inquiétude both have verbal forms (se soucier, s'inquiéter) and adjectival forms (soucieux/soucieuse, inquiet/inquiète): 

Sans se soucier [or: s'inquiéter] de dévoiler ses sentiments.

Without worrying about revealing her feelings.

Caption 7, Vous avez du talent Paulin - "Elle"

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Donc si vous êtes un petit peu soucieux [or: inquiet] de votre santé...

So if you're a little bit concerned about your health...

Caption 16, Voyage dans Paris - Cité Florale

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Un souci is also "a problem" or "an issue" you might have with something—for instance, if there's something wrong with a bike you've rented: 

...si y a aucun souci avec les pédales.

...if there's any problem with the pedals.

Caption 34, Amal - Vélib

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Et si y a le moindre souci avec un vélo...

And if there's the slightest issue with a bike...

Caption 57, Amal - Vélib

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But un souci doesn't always involve a sense of frustration or anxiety. It can also mean "a concern," as in something you really care about and pay a lot of attention to. 

Le souci du détail est un dogme.

Concern over detail [or: Attention to detail] is a dogma.

Caption 27, Le Journal Chocolats

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Nous avons un grand souci de l'environnement. 
We have a great concern for [or: We really care about] the environment. 

There are also the expressions par souci de and dans un souci de, both meaning "in the interest of" or "for the sake of":

Si une partie de Lyon a été retenue, c'est d'abord par souci de [or: dans un souci de] cohérence.

If a portion of Lyon has been contained, it is primarily for the sake of coherence.

Caption 11, Le Journal - La grippe aviaire - Part 2

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BANNER PLACEHOLDER

Finally, souci is also the word for "marigold." So while the informal expression pas de souci most often means "no worries," it can also mean "no marigolds"!

The adjectives sensé(e) and censé(e) are easy to confuse, since they have the same pronunciation and almost the same spelling (in other words, they're homophones). Sensé(e) is related to the English word "sense," and means "sensible," "reasonable," or "sane": 

BANNER PLACEHOLDER

J'étais face à trois personnes que

I was facing three people whom

je considérais comme étant parfaitement sensées.

I considered to be perfectly sane.

Captions 80-81, Le Jour où tout a basculé - Notre appartement est hanté

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Censé(e) might remind you of the words "census," "censor," or "censure," but it means something quite different. It's the word for "supposed," as in "supposed to do something." Just like "supposed to," it's nearly always preceded by the verb "to be" (être) and followed by an infinitive: 
 

On est censé... faire réparer des objets qui ont quelques problèmes.

We're supposed to... bring items that have some problems for repair.

Caption 2, Actus Quartier - Repair Café

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On était censé n'avoir aucun souci,

They were supposed to have no concerns,

avoir des centrales complètement fiables.

to have totally reliable power plants.

Caption 25, Manif du Mois - Fukushima plus jamais ça

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Alors que la police, elle est censée être là pour nous protéger.

While the police are supposed to be there to protect us.

Caption 14, Banlieues françaises - jeunes et policiers, l'impossible réconciliation?

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You can always say supposé(e) instead of censé(e), which might be a little easier to remember:

...son fameux pont

...its famous bridge,

qui était supposé être un lieu où [on] profitait de beaux panoramas.

which was supposed to be a place where you enjoy beautiful panoramas.

Captions 26-27, De nouvelles découvertes avec Marion - Le parc des Buttes Chaumont

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Or you can use the verb devoir, especially in the past tense:

...bien qu'elle se demanda

...although she wondered

en quoi cela devait l'aider à se rendre au bal.

in what way that was supposed to help her get to the ball.

Captions 47-48, Contes de fées - Cendrillon

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BANNER PLACEHOLDER

Whichever version of "supposed to" you use is perfectly sensé!