With an increase in the awareness of polymer viscoelasticity, several researchers in the textile industry have conducted rheological experiments to investigate the polymeric materials they deal with. However, the experimental results can be interpreted meaningfully when the polymeric materials are processed and analyzed based on viscoelastic theory. This review first describes the fundamental theories of linear viscoelasticity. Moreover, it provides various examples of linear viscoelastic studies on polydisperse polymer melts, polymer solutions, polymer blends, and reacting systems. The types of experiments depend on the measured viscoelastic functions. Viscoelastic functions are mathematically interconvertible within a linear viscoelastic range. However, numerical data processing is necessary to practically apply theoretical relations to experimental results. Here, we review several useful numerical methods and algorithms. We hope this review could be a helpful guide for researchers analyzing the viscoelasticity of textile materials.