Single-chain magnets (SCM) are a novel class of molecular magnetic materials exhibiting slow magnetic relaxation, which arises from large uniaxial type magnetic anisotropy, strong intrachain and very weak or negligible interchain magnetic interactions. Although more than 20 examples of SCM have been reported, the controlled synthesis of SCM is still a challenge. Here we review the three strategies for the construction of SCM, highlight typical examples, discuss the role of intrachain and interchain interactions on the overall magnetic behavior of SCM as well as how to control or tune these interactions. For each strategy we present the advantages/shortcoming and then point out the main directions that remain to be developed in the field.