Abstract: Fractures are ubiquitous in the subsurface, and they provide dominant pathways for fluid flow in low permeability formations. Therefore, fractures usually play an essential role in many engineering fields, such as hydrology, waste disposal, geothermal reservoir and petroleum reservoir exploitation. Since fractures are invisible and have variable sizes from micrometers to kilometers, there is limited knowledge of their structure. We aim to deepen the understanding of fracture networks in the subsurface, from their topological structures, hydraulic connectivity and characteristics at different scales. We adopt the discrete fracture network method and develop an efficient C++ code, HatchFrac, to make in-depth investigations possible. We start by generating stochastic fracture networks by constraining fracture geometries with different stochastic distributions. We apply the percolation theory to investigate the global connectivity of fracture networks. We find that commonly adopted percolation parameters are not suitable for characterizing the percolation state of complex fracture networks. We implement the concept of global efficiency to quantify the connectivity and evaluate the impact of fracture geometries on the connectivity of fracture networks. Furthermore, we constrain the fracture networks with geological data and geomechanics principles. We investigate the correlation of fracture intensities with different dimensionality and find that it is not feasible to have correct 3D intensity parameters from 1D or 2D samples. We utilize a deep-learning technique and propose a pixel-based detection algorithm to automatically interpret fractures from raw outcrop images. Interpreted fracture maps provide abundant resources to investigate fracture intensities, lengths, orientations, and generations. For large scale faults, we develop a method to generate fault segments from a rough fault trace on a seismic map. Accurate fault geometries have significant impacts on damage zones and fault-related flow problems. For small scale fractures, we consider the impact of fracture sealing on the percolation state of orthogonal fracture networks. We emphasize the importance of non-critically stressed and partially sealed fractures, which are usually neglected because they show non-hydraulic responses. However, with significant stress perturbations, those non-critically stressed and partially sealed fractures can also contribute to the production by enlarging the stimulated reservoir volume.