This is an age-old question and one that has a very detailed answer. In the technical sense, their debt is their debt, and it will have no effect on your credit.
However, there are some things to consider in regard to the future payment of the debt. This is definitely something that should be discussed in detail before walking down that aisle.
When a person establishes their credit record, it is exactly that, theirs. Credit reports do not come out for couples, each person is responsible for their own credit history.
If the debt was incurred in their name only, they are solely responsible for that debt. However, it will affect your ability to buy things jointly in which credit is needed and it will affect future household finances.
If you are truly happy with this person, the debt should not stop you from marrying them. BUT, it is recommended that you sit down together to go over finances.
If they have a heavy debt load, their contribution to the household bills may not be equal. Will you continue to make them pay the debt on their own or will that debt get folded into the monthly budget?
In addition to discussing the monthly budget, it may be time to consider cancelling all of their credit cards, or at the very least, cutting them up until the debt is clear.
If it is another type of debt, such as a student loan, you may want to reach out to the agency as see if the terms of payment can be reworked to better suit the monthly budget.
Falling into a relationship with someone deep in debt is not all that uncommon these days. The costs of education are rising as well as the rate of unemployment.
This is a deadly combination in that people are graduating with much less chance of being able to land a job that can cover their debt commitment.
It is best to get everything out on the table right from the start and figure a way to make it work.