The pressure function plays a fundamental role in the thermodynamic formalism of dynamical systems. McMullen used the convexity of pressure functions to define a metric, called the pressure metric, on the Teichmüller space and showed it is a constant multiple of the Weil-Petersson metric. Following Sullivan's dictionary, McMullen extended this approach to define a metric on the space of Blaschke products. In this talk we will first explore early contributions by Bridgeman-Taylor and McMullen to the theory of pressure metrics, alongside recent developments in more general settings. We will then discuss unresolved questions and partial results on pressure metrics for hyperbolic components of rational maps in complex dynamics. This is based on joint work with Yan Mary He and Homin Lee.