Caso seems like an easy cognate, and it is, indeed, especially when we say something like in ogni caso (in any case). 

In ogni caso, è una cosa veramente molto tipica.

In any case, it's a really typical thing.

Caption 40, Anna e Marika Un Ristorante a Trastevere

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Or, caso can mean "case," as in a criminal case.

Quindi voi o risolvete il caso in due giorni, o io sono costretto a togliervelo.

So either you solve the case in two days, or I will be forced to take it away from you.

Captions 80-81, I Bastardi di Pizzofalcone EP1 I Bastardi - Part 21

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But we also find the word caso meaning "chance" or "fate." That's when things start getting a little fuzzy.

Signora, per caso vendete questo tipo di palle di vetro?

Ma'am, by chance do you sell glass balls of this type?

Caption 23, I Bastardi di Pizzofalcone EP1 I Bastardi - Part 23

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Here, we could say, "As chance would have it..."

E guarda caso sembra raffigurare le tre generazioni:

And strangely enough, it seems to represent the three generations:

Caption 14, A Marsala Salvo Agria

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Caso can refer to "the circumstances," so when we say: È il caso, we mean that "circumstances call for something."

Però forse è il caso di farci un salto, eh?

But, maybe we should hop on over there, huh?

Caption 84, Il Commissario Manara S1EP6 - Reazione a Catena - Part 4

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In English, sometimes we just use "should." 

We often use this expression in the negative. Non è il caso... This means something is not called for. It's not the right thing to do, best to avoid it. Sometimes non è il caso can mean, "Don't bother," or "It's not necessary." 

Grazie, grazie, ma non è il caso. -Sarebbe meraviglioso, bellissimo!

Thanks, thanks, but it wouldn't be right. -It would be marvelous, great!

Caption 97, Il Commissario Manara S1EP10 - Un morto di troppo - Part 4

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That's not all, but we'll pick up this topic again in another lesson. Thanks for reading!