Rational maps are mathematical functions that represent a relationship between two complex variables. They can be expressed as the ratio of two polynomials, where the numerator and denominator are both polynomial functions. These maps are often studied in the field of complex dynamics, where they help in understanding the behavior of iterated functions. In the context of complex analysis, rational maps can exhibit interesting properties, such as fixed points and periodic points. They are used to explore concepts like Julia sets and Mandelbrot sets, which illustrate the intricate structures that arise from the iteration of these functions.