Through the Healthcare FSA or Healthcare Limited FSA, you can claim eligible expenses for you, your spouse, and your dependent children under the age of 26.
 
Through the Dependent Care FSA, you can claim eligible daycare and before/after school care expenses for a qualifying dependent. The IRS defines a qualifying dependent as:

• Your child who is under the age of 13.
• Your spouse who is not physically or mentally able to care for themself and has lived with you more than half the year.
• A person who is not physically or mentally able to care for themself and has lived with you more than half the year.