In addition to a dynamic surface for strength and balance exercises the ball is also a great stretching prop. One of the most basic and obvious stretches is to simply to lie over the ball.
The supine lateral roll like many other Swiss ball exercises is more about balance and stability than brute strength. In this exercises your stabilizer muscles to prevent your torso from bending and twisting as roll you upper back and shoulders across the ball.
The ball is great for rotational exercises and prone torso twists are no exception. For this intermediate to advanced exercise you must have the lower abdominal and core strength to hold your back in alignment as you twist side to side.
The pike press with the Swiss ball is an intermediate to advanced exercise and requires significant upper body strength. Balance and coordination come into play but strength is usually the limiting factor.
Bridging movements are some of my favorite Swiss ball exercises. They generally offer a wide progression difficulty. I've used the bent knee bridge with de-conditioned clients in their seventies and challenged young athletes with the advanced variations.
Reverse Extensions are another way to target your lower back and core with the Swiss Ball. Reverse Extension flex and extend your lumbar spine using the weight of your lower body for resistance.
Reverse crunches on the Swiss Ball allow you to train your abdominal through a full range of motion while challenging your balance and coordination. This movement requires more lower abdominal strength than regular crunches.
Leg Lifts build strength, endurance, and coordination of the lower abdominal wall and test the recruitment of important core muscles like the transverse abdominus.