Is a critical failure on a natural 1 a rule or house rule?

There’s a question about this relating to 3.5e, but I couldn’t find one for 5e.

According to RAW, is a natural 1 a critical failure? And if so, under what scenarios does it apply, and what is the expected result?

One of my players is dissatisfied with my calls relating to 1’s* but I don’t have my books handy and I’m having trouble figuring out if the whole shebang is a very popular houserule or actually in RAW.

*I have a feeling that I am likely in the wrong here and it’s more of a same-page issue than a mechanics one, but I want to check what the book’s ruling is before we sit down to have a conversation about it. Our table dynamics aren’t the question here; I just need to know the mechanics to make an informed decision.