What are the advantages of a diesel engine?

It lasts a looong time if cared for properly.

They are great for applications where torque is needed to get work done. 

High torque at low revs. Better efficiency. Back in the 1970's and earlier, diesel fuel was way cheaper than gasoline....not anymore.

Well, they are a complete waste of money in light duty uses. The fuel is a lightly refined crude oil and gells up in cold temperatures so you have to add stuff like "Howes" to prevent gelling in the cold months. Or you have to use a blended diesel fuel that is part Diesel #1 mixed with Diesel #2. They are noisy, the exhaust smells like an oil rig fire, and the parts when needed are super expensive. 

Way more torque than a gasoline engine. Will last much longer with less maintenance. Some have gone 1,000,000 miles before needing an overhaul. 

Are you talking about now or in the past, they used to be fairly dirt simple but now since they have electrified them it's like game over

Torque, lots of torque.  Did I say torque?

No ignition system

Higher fuel efficiency

Higher torque curves at lower RPM

Longevity