Graph theory has provided chemists with a variety of very useful tools, and one of such tools is the topological indices. In the field of chemical graph theory and mathematical chemistry, a topological index also known as a connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Among the oldest and most famous topological index, the first and the second are Zagreb indices. Zagreb indices possess many interesting properties. This chapter provides some results of Zagreb indices, for chemical graphs and nanostructures. The Zagreb indices and their variants have been used to study molecular complexity chirality, ZE-isomerism and heterosystems whilst the overall Zagreb indices exhibited a potential applicability for deriving multilinear regression models. Mathematical properties of the Zagreb indices have also been studied.