Bezier curves are mathematical curves used in computer graphics and design to create smooth and scalable shapes. They are defined by a set of control points, which determine the curve's direction and shape. The simplest form, a linear Bezier curve, connects two points, while more complex forms can involve multiple points to create intricate designs. These curves are widely used in applications like Adobe Illustrator and AutoCAD for drawing and animation. They allow designers to manipulate shapes easily, providing flexibility in creating everything from simple lines to complex paths. Their smoothness and scalability make them essential in digital art and typography.