The main problem with most jet airliners is that the engines are placed close to the ground. If the field is not paved, this increases the risk of damage to the engines from ingesting FOD (foreign object debris).
There are, however, jets that can operate from un-paved fields.
The 737-200 has an option called a "gravel kit." Despite having engines close to the ground, this kit helps to prevent the engine from sucking in FOD, which allows the aircraft to operate off of gravel runways. It also includes an addition to the nose gear to help prevent gravel from getting kicked up. For this reason, airlines like Canadian North still operate multiple 737-200 aircraft in order to provide service to airports with gravel runways.
High-wing aircraft are better suited for this type of mission (see Pros and cons of high-wing vs. low-wing design). The C-17 is a military airlift designed to operate from remote airfields. Its wings are placed above the fuselage rather than below, which allows the engines to be mounted further above the ground. The IL-76 is a Russian aircraft of a similar configuration that also operates out of unpaved fields.
Aircraft with engines mounted on the rear fuselage also protect the engines from ingesting FOD. The new Pilatus PC-24 jet advertises the ability to operate from unpaved strips. Older aircraft like the 727 or the Tu-154 have this engine placement as well, and both can operate from unpaved fields.
737-200 landing on a gravel runway. The gravel kit is visible as the small extension just below the front of the engine, and the addition to the rear of the nose gear.