[tomxtr]

You don't list your current employer as a reference, but you absolutely list them on your resume. It is probably best to mention to the interviewer not to contact your current employer. Most states are right-to-work states which means that they can fire your ass for no reason, so why give them a reason. However, most jobs will just give you a hard time if they find out that you are looking. If they fire you and you file for unemployment and win, then their unemployment rates go up.

If they extend you an offer and you accept, they might call you current employer to verify your employment status.