Self-assembly is a phenomenon broadly observed in nature where a vast number of various molecules spontaneously synthesize complex structures. In this paper, aiming at realizing highly autonomous self-assembly systems, we discuss fundamental issues attributed to self-assembly systems that employ magnetism as a driving force. We first introduce some examples from our case studies, in which the models all subscribe to a distributed approach, and thus lack central control. Then we categorize them by their type of magnet attachment. The discussed issues include several fundamental properties, such as the effect of morphology, stochasticity, the difference between 2D models vs. 3D models, emergence, allostericity, and parallelism. The obtained conclusions support our stance, which is that the appropriate morphology lightens the control cost for the assembly, providing primal but engaging instances of magnetic self-assembly systems that warrant further study.