Recently, a new class of nano-magnets has been discovered and called single-chain magnets (SCMs) by analogy to the single-molecule magnets (SMMs). These materials are composed of magnetically isolated chains that can be individually magnetized. As purely one-dimensional systems are known to have a long-range order only at T∈=∈0 K, these SCM materials remains in their paramagnetic state at any finite temperature. Nevertheless, the combination of a large uni-axial anisotropy and large magnetic interactions between the high-spin magnetic units of the chain promotes long relaxation times and the system can behave as a magnet. Although the presently available materials possess long relaxation times only below about 10 K, the limitations to produce SCMs compatible with industrial applications seem less severe than for SMMs. This is one of the reasons explaining why the chemistry and the physics on SCMs have quickly become a very active field. In the first part of this review, we have summarized the last developments on the theoretical understanding of the SCM behavior. In these systems, the key analysis of the magnetic properties is the comparison between static susceptibility and dynamic data that leaves no arbitrary parameter and allows an unambiguous identification of a SCM. The second part of this review is devoted to the experimental SCM systems reported so far. In particular, selected examples are presented to illustrate how it is possible to characterize experimentally a material with SCM properties.