Your foreign national spouse entered the United States illegally (with no authorization).
With very limited exceptions, foreign nationals cannot get a green card based on marriage if they entered the United States illegally. If you fill out an application without consulting an attorney beforehand, then you have simply notified Immigration about your spouse's current illegal status and location.
You have not yet filed an application based on your marriage to a US citizen or LPR because of marital problems.
This is the perfect time to consult an attorney. You may qualify to petition for yourself instead of having your spouse petition for you. Do not assume that you cannot obtain a green card because your valid marriage has gone sour.
You are a conditional resident and currently having marital problems.
If Immigration granted conditional residence based on a marriage that was less than two years old, then you will have to file a petition with your spouse to remove conditions. Sometimes, those cases require another interview. If you are having problems in your marriage, it might be possible to get a waiver. So, your spouse does not have to attend the interview with you and you could still get a permanent green card. Waivers are also available for the entire case so even the spouse's signature is not required.
Your application was not approved based on an allegation of fraud.
Contact an attorney immediately. It is best to address your case while evidence of your valid marriage is fresh. Do not assume that you can put this behind you because Immigration left you alone. Marriage fraud is a serious allegation and you will be barred from filing a subsequent application with a new spouse even though you were not convicted. A failed marriage does not mean your application is worthless as well. Remember, more than half of the marriages in this country end in divorce.
You obtained your LPR status through marriage to a first spouse and want to petition for a second spouse.
Unfortunately, the law prevents the application with your new spouse from being approved within 5 years from the date you initially got your LPR status through your first marriage. The application can be filed, but will remain "pending" until it can be approved. Also, your second marriage will probably be scrutinized more heavily due to suspicion of fraud. In this situation, it is extremely important for a qualified immigration attorney to review your application and prepare both of you for the interview. The last thing you need is to file an application with your new spouse that results in a fraud accusation.