Amyloid fibrils are associated with a number of debilitating diseases, including Alzheimer's disease and variant Creutzfeldt-Jakob disease. The elucidation of the structure of amyloid fibrils is an important step toward understanding the mechanism of amyloid formation and developing therapeutic agents for amyloid diseases. Despite great interests and substantial efforts from various research communities, deriving high-resolution structures of amyloid fibrils remains a challenging problem, due to the insolubility and non-crystalline nature of the fibrils. An array of experimental methods, such as electron microscopy, fiber diffraction, hydrogen-deuterium exchange, solid-state NMR, electron paramagnetic resonance spectroscopy and biochemical approaches, have been explored to study the problem, having yielded considerable amount of, though still partial, information about the fibril conformation. Computational modeling techniques can be used to predict and build structural models of amyloid fibrils, utilizing the available experimental data. Here, we describe a few computational methods for modeling of aggregate and fibril structures with a focus on protein threading-based approaches and discuss the challenging issues ahead.