Abstract: Hitchin in 1987 introduced the map now named after him, and showed that it defines a completely integrable system in the complex-algebraic sense. Subsequently Beauville, Narasimhan and Ramanan constructed a correspondence -- indeed nowadays refered to as the BNR correspondence -- which among other things characterizes the generic fiber of a Hitchin map as a compactified Jacobian. In this talk, we will review the geometric properties of Hitchin maps and introduce their generalizations to parabolic (Higgs) bundles over an  algebraically closed field.