Lithium-ion batteries (LIBs) are currently one of the most important electrochemical energy storage devices, powering electronic mobile devices and electric vehicles alike. However, there is a remarkable difference between their rate of production and rate of recycling. At the end of their lifecycle, only a limited number of LIBs undergo any recycling treatment, with the majority go to landfills or being hoarded in households. Further losses of LIB components occur because the the state-of-the-art LIB recycling processes are limited to components with high economic value, e.g., Co, Cu, Fe, and Al. With the increasing popularity of concepts such as “circular economy” (CE), new LIB recycling systems have been proposed that target a wider spectrum of compounds, thus reducing the environmental impact associated with LIB production. This review work presents a discussion of the current practices and some of the most promising emerging technologies for recycling LIBs. While other authoritative reviews have focused on the description of recycling processes, the aim of the present was is to offer an analysis of recycling technologies from a CE perspective. Consequently, the discussion is based on the ability of each technology to recover every component in LIBs. The gathered data depicted a direct relationship between process complexity and the variety and usability of the recovered fractions. Indeed, only processes employing a combination of mechanical processing, and hydro- and pyrometallurgical steps seemed able to obtain materials suitable for LIB (re)manufacture. On the other hand, processes relying on pyrometallurgical steps are robust, but only capable of recovering metallic components.