I'm wondering if as a phd student, typically people should mention the grants in their CV. For example, even some small grants that you get when you attend a conference.
Just to be clear, it depends on what you are calling grants. If you apply to an (internal or external) program that has some sort of name (e.g., University Student Travel Grant), then yes, this counts as something you can put under the "Awards" section of your CV. (Incidentally, related question: List dollar amount of small grants on C.V.?)
If, however, you mean you got money from your advisor's grant, or the conference had a grant that provided you travel money (even if you had to request it), or the university automatically funds you, that does not count as an award.