A hardship license (in Missouri) or restricted driving permit (in Illinois) is a limited driving privilege issued during a license suspension. It allows driving for essential purposes (work, school, medical care, and certain family obligations) even when the regular license is suspended.
In Missouri, a Limited Driving Privilege (LDP) is available after most DWI-related suspensions, sometimes from the date of arrest, often requiring an ignition interlock device (IID). The application goes through the circuit court in your county of residence.
In Illinois the Monitoring Device Driving Permit (MDDP) is available to most first-time DUI defendants, but under 625 ILCS 5/6-206.1 it cannot take effect before the 31st day of the statutory summary suspension. There is no driving relief during those first 30 days. The MDDP then allows unrestricted driving in a vehicle equipped with a BAIID, and the statute lists categories of first offenders who are ineligible entirely.
Hardship licenses don't restore full driving privileges. They restrict the times, routes, and purposes of driving. Violations can result in extending the underlying suspension or new criminal charges.