Liquid Composite Molding (LCM) is a manufacturing process for fiber-reinforced composite materials, in which a dry fiber structure is infiltrated by a liquid polymer. During process simulation, the flow of a liquid polymer through the fiber structure is governed by flow phenomena at different spatial scales spanning from micrometers to meters. The first and vital step in this process simulation is the estimation of permeabilities of the fibrous microstructure. Conventional methods that compute permeability by solving the Stokes equation can be slow and computationally expensive for large 3D fibrous microstructures. Thus, a fast emulator for permeability prediction on the microscale is desirable. In this work, data-driven emulators were developed using machine learning and deep learning to predict the permeability of 3D fibrous microstructures. Two categories of emulators: feature-based and geometry-based models were developed and evaluated based on a benchmark permeability dataset.