Runge-Kutta methods are a family of numerical techniques used to solve ordinary differential equations. They provide a way to approximate the solutions by breaking the problem into smaller steps, allowing for greater accuracy than simpler methods like Euler's method. The most common version, known as the fourth-order Runge-Kutta method, calculates intermediate values to improve the estimate of the solution at each step. These methods are widely used in various fields, including physics, engineering, and computer science, due to their effectiveness and ease of implementation. By adjusting the number of steps and the method's order, users can balance accuracy and computational efficiency for different problems.