Fractional derivatives, a widely recognized mathematical tool, have gained considerable attention in recent decades owing to their non-local behavior, particularly suitable for capturing anomalous diffusivity. They find application in various real-world scenarios that range from the interaction between particles and fields within plasma to the dynamics of networks in human environments. While the presence of a fractional derivative in a differential model can result in a better physical description, it also poses significant challenges in numerical treatment. Specialized strategies, including discretization methods and numerical solvers, are required to address such challenges effectively. This presentation aims to offer insight into the topic, with a specific emphasis on the numerical linear algebra obstacles it entails.