Single-Molecule Magnets (SMMs) are finite molecular species that display slow relaxation of their magnetisation, equivalent to a magnetic memory effect. Here we give an overview of how SMM behaviour can arise from the spin properties of a giant molecular spin or unpaired electrons on a single metal centre. We outline the criteria for obtaining SMM properties, and how these have developed through theoretical insight to lead to the rapid advancement of SMM performance. We discuss the progression of the field from the original Mn12 polymetallic cluster, to carefully engineered coordination complexes of Ln ions. Classes of compounds discussed include 3d, 3d-4f and 4f polymetallic clusters, 3d and 4f monometallic complexes, and homo-and hetero-metallic exchange-coupled SMMs, including those bridged by radical ligands and/or encapsulated in endohedral fullerenes. The state-ofthe-art in SMMs is discussed, leaving the reader with an up-to-date understanding of theory and synthetic design, with references to comprehensive reviews.For readers new or returning to the area, we highlight the standard experiments used to characterise SMMs -including magnetic hysteresis, zero-field cooled/field cooled magnetic susceptibility, alternating current susceptibility and magnetisation decay measurements. We highlight the common pitfalls often encountered in the literature in measurements, data analysis and structural correlation of properties. We aim to provide a clear background for relaxation mechanisms in SMMs and the quantification of performance using energy barriers, blocking temperatures and relaxation rate. The reader is directed towards a series of proof-ofconcept publications which have spearheaded the implementation of SMMs towards future applications in high density data storage, quantum information processing and spintronics.