Manual fault mapping from 3D seismic data is a time-consuming task. A plethora of seismic attributes has been proposed to enhance the discontinuity measures associated with faults. However, faults viewed through these attributes appear more like trends than well-defined, continuous surfaces, posing obstacles to the automation of the fault modeling process. This thesis explores the use of Competitive Learning techniques in fault extraction and visualization. The proposed strategy starts with a pre-computed fault attribute and consists of three steps. In the first, the uniformly sampled 3D fault attribute data are converted into a graph using Growing Neural Gas, a Competitive Learning algorithm. In the second step, the graph is submitted to a segmentation process in order to extract a set of subgraphs, each one compatible with a fault surface. In the third step, the Open Neural Meshes algorithm is used to build a triangulated mesh for each previously identified surface. Open Neural Meshes is a Competitive Learning algorithm proposed in this thesis, which builds a mesh from a probability function with no-hole open surface topology. Examples with 2D and 3D, synthetic and real data are presented. Another Competitive Learning application introduced in this thesis is the generation of geologic meshes. These meshes can be used to simulate fluid flows in subsurface reservoirs.