There are several popular types of corsets, including underbust, overbust, waist training, and fashion corsets. Underbust corsets are designed to sit below the bust and are often worn as part of a layered look. Overbust corsets cover the bust and are often worn as a standalone garment. Waist training corsets are designed to gradually reduce the waistline over time, while fashion corsets are often made with decorative materials and may not have the same shaping abilities as other types of corsets.