In this paper, we propose a thorough experimental and theoretical investigation of memory-cell structures employing discrete-trap type storage nodes, using either natural nitride traps or semiconductor nano-crystals, thus operating with a small finite number of electrons, A detailed account of static and dynamic charging/discharging phenomena occurring in these devices is given, based on bias-, time-, and temperature-dependent measurements. A comprehensive interpretation of experimental results is proposed by means of a physical modeling, In particular, two different models are proposed. The first one consists in a modified floating-gate-like approach, while the second one is a trap-like approach, relying on the Shockley-Read-Hall statistics, Using these two approaches, some general behavior laws for memory operation are formulated. Considerations on the suitability of each model on the particular structures are suggested.