eSCAPE is an open-source Python-based landscape evolution framework that computes over geological time (1) landscape dynamic, (2) sediment transport from source to sink, and (3) continental and marine sedimentary basins formation under different climatic and tectonic conditions. eSCAPE is cross-platform, distributed under the GPLv3 license and available on GitHub. Simulated processes rely on a simplified mathematical representation of landscape processes - the stream power and creep laws - to compute Earth's surface evolution by rivers and hillslope transport. The main difference with previous models is in the underlying numerical formulation of the mathematical equations. The approach is based on a series of implicit iterative algorithms defined in matrix form to calculate both drainage area from multiple flow directions and erosion/deposition processes. eSCAPE relies on PETSc parallel library to solve these matrix systems. Along with the description of the algorithms, examples are provided and illustrate the model current capabilities and limitations. eSCAPE is the first landscape evolution model able to simulate processes at global scale and is primarily designed to address problems on large unstructured grids (several millions of nodes).