While Chapter 7 will discharge most debts, including your credit card debts and medical bills. Those debts which are not dischargeable include Alimony, maintenance and support for a spouse and children, student loans, most taxes that are owed for the last 3 years, criminal fines and penalties as well as restitution orders. In addition all taxes owed for the past three years prior to filing are not dischargeable. Taxes owed for more than three years prior to filing, may be dischargeable under a complicated formula. Also Fraud and Drunk driving claims are not dischargeable.
Finally, if you took on an obligation to pay a debt through a divorce settlement, you can discharge the debt to the original creditor, however, your obligation to your ex-spouse is not dischargeable. So if you promise to pay the Discover Card and file for Bankruptcy, the Discover Card debt can be discharged, however, if Discover sues your ex-spouse he or she can then bring a claim back against you for the amounts he or she paid to Discover.