1. Have been unable to consent to the marriage (ex: underage or incapacitated and even then if you continued to live as husband and wife after you became 18 or had capacity this may not apply).
2. One of you was already currently legally married to someone else (bigamy. Again there are even some exceptions to this.)
3. Fraud (they lied about their identity, immigration status, etc).However proving fraud, the most commonly checked annulment box is incredibly difficult. Generally we sit down with the client and discuss whether the costs associated with asking for the annulment, even if you succeed are worth the time, cost, and effort to get one. In most cases the answer is no.
4. Mental incapacity. This generally refers to the time when they consented at the marriage, but can be looped in with fraud in regards to them not disclosing a serious mental disorder. This is often difficult to get the judge to approve though, although I have seen it when both parties agree to an annulment and the marriage and courtship were fairly short.
Even if you meet one of these requirements, you still need to file within the required time period to get an annulment instead of a dissolution (divorce).In most cases, this time period is within 4 years of marriage.
If you meet the requirements, then the judge is like a magician and *poof* your marriage never happened. This can also create a mess regarding property distribution since there will be no community property assets or debts if the marriage never existed.