Recent breakthrough experiments have identified fractional Chern insulator phases in two-dimensional platforms. Despite the absence of an external magnetic field, these phases break time-reversal symmetry and exhibit strong similarities to the celebrated fractional quantum Hall effect. They suggest a broad analogy between topological flat bands and Landau levels. For a specific class of experimentally relevant bands, a mapping has even been established between these bands and conventional Landau levels. This mapping is generally linked to an orbital winding of the band, called a skyrmion, in analogy with non-trivial spin texture in magnetic systems. The aim of this internship is to investigate the formation of orbital skyrmions in topological flat bands. By solving continuum models with superlattice (moiré) potentials, the robustness of the topological orbital skyrmions will be studied for generic bands beyond the ideal case. One objective is to explore how the Landau level duality between real-space and momentum topology extends to genuinely topological bands. Additionally, electrons interactions may stabilize a Wigner crystalline structure with topological properties. Using a Hartree-Fock approach, the orbital skyrmion texture of this symmetry-broken state will be then investigated. Typical examples will include simple models of twisted bilayer graphene, twisted transition metal dichalcogenides, and rhombohedral multilayer graphene.