Slow relaxation of the magnetization (i.e., "magnet-like" behavior) in materials composed of magnetically isolated chains was observed for the first time in 2001. This type of behavior was predicted in the 1960s by Glauber in a chain of ferromagnetically coupled Ising spins (the so-called Glauber dynamics). In 2002, this new class of nanomagnets was named single-chain magnets (SCMs) by analogy to single-molecule magnets that are isolated molecules displaying related superparamagnetic properties. A long-range order occurs only at T = 0 K in any pure one-dimensional (1 D) system, and thus such systems remain in their paramagnetic state at any finite temperature. Nevertheless, the combined action of large uniaxial anisotropy and intrachain magnetic interactions between high-spin magnetic units of the 1D arrangement promotes long relaxation times for the magnetization reversal with decreasing temperature, and finally at significantly low temperatures, the material can behave as a magnet. In this Forum Article, we summarize simple theoretical approaches used for understanding typical SCM behavior and some rational synthetic strategies to obtain SCM materials together with representative examples of SCMs previously reported.