In this talk, we will explore the results of spin and orbital Hall effects in two-dimensional (2D) topological materials. We have conducted high-throughput calculations to determine the spin (SHC) and orbital (OHC) Hall conductivities across hundreds of 2D materials, aiming to understand the relationship between these Hall effects and topological properties. Initially, we will discuss the OHC plateau observed within the insulating gap of 2D transition metal dichalcogenides (TMDs). These TMDs are characterized as higher-order topological insulators (HOTIs) using a Z4 topological invariant. Employing general symmetry principles, we will establish a linkage between these phenomena, highlighting potential applications in spin-orbitronics. A broader perspective will be provided by examining the SHC and OHC data compiled from an extensive 2D materials database.