Nanofibers functionalized by metal nanostructures and particles are exploited as effective flexible substrates for surface-enhanced Raman scattering (SERS) analysis. Their complex three-dimensional structure may provide Raman signals enhanced by orders of magnitude compared to untextured surfaces. Understanding the origin of such improved performances is therefore very important for pushing nanofiber-based analytical technologies to their upper limit. Here, we report on polymer nanofiber mats which can be exploited as substrates for enhancing the Raman spectra of adsorbed probe molecules. The increased surface area and the scattering of light in the nanofibrous system are individually analyzed as mechanisms to enhance Raman scattering. The deposition of gold nanorods on the fibers further amplifies Raman signals due to SERS. This study suggests that Raman signals can be finely tuned in intensity and effectively enhanced in nanofiber mats and arrays by properly tailoring the architecture, composition, and light-scattering properties of the complex networks of filaments.