Single domain magnetic nanoparticles (MNPs) have been a vivid subject of intense research for the last fifty years. Preparation of magnetic nanoparticles and nanostructures has been achieved by both bottom-up and top-down approaches. Single domain MNPs show Néel-Brown-like relaxation. The Stoner-Wohlfarth model describes the angular dependence of the switching of the magnetization of a single domain particle in applied magnetic fields. By varying the spacing between the particles, the inter-particle interactions can be tuned. This leads to various supermagnetic states such as superparamagnetism, superspin glass, and superferromagnetism. Recently, the study of the magnetization dynamics of such single domain MNPs has attracted particular attention, and observations of various collective spin wave modes in patterned nanomagnet arrays have opened new avenues for on-chip microwave communications. MNPs have the potential for various other applications such as future recording media and in medicine. We will discuss the various aspects involved in the research on MNPs.