Generally speaking, if you had nothing to do with the debt (i.e., you didn't sign anything to acknowledge or assume it, didn't gain from it, and were not ordered by the court to satisfy it) during the marriage, then the creditor won't be able to go after you after the divorce. The creditor in such a situation has a connection with your spouse -- not you -- and could no more go after you than anyone else. For example, if your spouse signed a contract to buy a car, you never signed any papers for it, it wasn't titled in your name, you never drove it, and the judge didn't order you to make the rest of the payments, then you're almost certainly safe from any action by the creditor. If you cosigned the note, however, you're fair game for the creditor and there is little you can do in divorce court for protection.
Joint debts are a different story. In the example above, if you cosign the note, the creditor can come after you if your spouse doesn't pay -- usually regardless of what the divorce court says. If your spouse files for bankruptcy, you may end up paying a debt that your spouse agreed to pay in the divorce settlement. Your attorney can help protect you before the bankruptcy court from such financial abuse by making a substantive "debt-for-maintenance trade" in the divorce court. The language of this agreement can be very tricky and may make or break the protective shield. Be sure to work with an experienced attorney who is familiar with divorce and bankruptcy law.
Wes Cowell practices family law in Chicago and runs the Illinois Family Law and Divorce Center.