The paper chronologically describes the results of research on the flow of micro-encapsulated PCM (mPCM) and nano-encapsulated PCM (nPCM) slurry in heat-transfer systems. The focus is on three thematic groups: mPCM (nPCM) slurry flow pressure drop; the friction factor in the laminar, transient, and turbulent flow of slurry in the channels; and the assessment of the effectiveness of using the mPCM (nPCM) slurry in the context of improving heat-transfer coefficients but with increased pumping power. It was found that the number of publications devoted to the above-mentioned topics is very limited compared to the research on the thermal and rheological properties of the mPCM (nPCM) slurry, which has resulted in the lack of systematized knowledge about the influence of slurry concentration, particle size, materials, etc., for example, on the friction factor. It was found that the use of the mPCM (nPCM) slurry in heat-transfer systems may be proper, provided that an appropriate and sufficiently high flow rate is ensured.