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Self-assembly is a phenomenon broadly observed in nature where a vast number of various molecules spontaneously synthesize complex structures. In this article, prompted by the need for the realization of highly autonomous self-assembly systems that employ magnetism as a driving force, we discuss fundamental issues associated with magnetically driven self-assembly systems. 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 magnetic attachment. The issues discussed include several fundamental properties, such as the effect of morphology, stochasticity, the difference between two-dimensional models and three-dimensional models, emergence, allostericity, and parallelism. The conclusions obtained support our stance 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. [ABSTRACT FROM PUBLISHER]