Single-molecules magnets (SMMs) and single-chain magnets (SCMs) are thought to be the magnetic materials for next-generation storage devices since one molecule of an SMM or a chain of an SCM can behave as a "bulk magnet" exhibiting magnetic hysteresis. When designing new SMMs and SCMs, strong magnetic anisotropy must be incorporated so that they undergo slow relaxation of the magnetization, which causes magnetic hysteresis. Moreover, in the case of SCMs, intrachain interactions are necessary. The incorporation of organic radicals satisfies both requirements. Here we discuss examples of SMMs and SCMs containing organic radicals and their magnetic properties.