Check the manufacturer product page for your case... It'll state the maximum GPU length supported.
Then check the page for whichever GPU you're considering and see if the length is less that the max supported.
Some will state X clearance with Y front fans, others won't - so keep that in mind.
Unless it's a fairly compact or OEM case &/or an extremely long GPU though, a 1070 shouldn't present too many issues in a somewhat standard ATX or mATX case....