What do you call it when you refuse to give up on a particular task

In Dutch we've got the expression 'Vastbijten in'. It means you really get into a problem or some work. And you won't give up till it's resolved. I've been looking all over the web, but I've not been able to find an expression that comes close enough.

Is there a way of saying this en English? The Dutch expression is a verb phrase, so that would probably come closest.

Edit

Thank you all very much for your answers:). Since I can only accept one final answer, I feel the need to do some clarification. Initially I added the single word request, since the expression in Dutch is just one word (not including the preposition). However, that's very specific to the Dutch language and I'm mostly looking for an expression that comes closest. Therefore I feel that:

• to get one's teeth into Comes closest, it's actually almost an exact translation both literally and in meaning.

• indefatigable Is the best candidate when a single word is required(although the literal translation in dutch for this would be 'onvermoeibaar'). This also is an interesting choice since vastbijten can be used as noun(vastbijter), meaning an indefatigable person.

• to dig in Would be probably the American equivalent of to get one's teeth into. Also not one word, but approaching the meaning closest.

An almost-literal translation is to get one's teeth into something.

Work energetically and productively on (a task):
the course gives students something to get their teeth into

[ODO]

A slightly more prosaic alternative might be persevere; that connotes slightly less enthusiasm for the task at hand.

"persistent", "dogged", "indefatigable".

If you're looking for a single word, as your tag suggests, may I recommend:

indefatigable

never giving up or getting tired of doing something

an indefatigable defender of human rights

She was indefatigable in her search for the truth.

[From oxford]

Tooth and nail:

• with all one's resources or energy; fiercely:

  • We fought tooth and nail till the end.

  • The market has changed, but the major players are fighting tooth and nail to keep going the way things have been.

(Dictionary.com)

In American English a few common sayings are:

"dig in" - which would fit closely with the dutch expression

"come hell or high water" - meaning that no obstacle will stop your efforts

"In for the long haul" - expressing a commitment to finish what is started

Single word options:

relentless - literally "does not stop"

indefatigable - literally "does not tire" (this is a bit archaic to American ears)