Eikonal equations in metric spaces have strong connections with the local slope operator (or the De Giorgi slope). In this talk, we explore an analogous model based on the global slope operator, expressed as $G[u] = \ell$. In strong contrast with the classical theory, the global slope operator relies neither on the local properties of the functions nor on the structure of the space, and therefore new insights are developed in order to analyze the above equation. Under mild assumptions on the metric space $X$ and the given data $\ell$, we primarily discuss: (a) the existence and uniqueness of (pointwise) solutions; (b) a viscosity perspective and (c) a new integration formula based on the global slope of the given function.