Yes, Stromboli should be refrigerated if it's not consumed immediately. As a general food safety practice, perishable items containing ingredients like cheese, meat, or other fillings should be stored in the refrigerator within 2 hours of preparation. This helps prevent the growth of harmful bacteria. Once cooled, you can store Stromboli in an airtight container in the refrigerator for up to 3–4 days. If you want to keep it longer, consider freezing it, but keep in mind that the texture may be slightly different upon thawing.