Kettlebells are unique because of their ability to produce ballistic movements more easily than dumbbells or barbells. Ballistic movements are movements that produce maximum velocity and acceleration over the shortest amount of time. Every muscle of the body is working during a kettlebell swing, which leads to quicker overall body toning. Barbells also produce ballistic movements easily but they require much more coaching and mobility initially than the kettlebell swing.
Since the KB swing is a ballistic movement- safety is crucial, so your form must be accurate to eliminate the risk of injury; most common is low back pain. The neck is also subject to injury or strain if proper attention to the alignment of the spine is not present. All of this being said, the athlete should work with a professional Kettlebell certified coach before performing the swing on their own. The most common mistake by far is the athlete using a squat motion vs. a hinge motion. This compromises the lower back and knees especially. I also see rib flaring/mid back bend at the top of the swing. Adequate abdominal strength and proper breathing are crucial to avoid this mistake. The athlete must be able to perform a proper hip hinge/deadlift before performing a swing. Once proper form is insured- the possibilities are boundless.
The Russian KB swing is in my opinion much safer and equally as effective as the American swing. The Russian swing stops at chest level while the American swing continues overhead. I love the American swing as a progression to the swing to add variety and an added level of difficulty/skill for the athlete. The overhead swing (American swing) also requires a certain level of shoulder and thoracic spine mobility, which unfortunately isn't common for the majority of athletes who have professions outside of the fitness world.
Single arm swings are a great variation to work anti-rotation and oblique/lat strength and add a level of difficulty to keep the athlete in a flow state once the 2 arm swing has become second nature. Double bell swings are great to add more of a strength component to the swing as well as really firing up the glutes and hamstrings.