Precise control over the monomer sequence of a polymer backbone, resulting in a sequence-defined polymer (SDP), is a crucial parameter for tuning the structures, properties, and functions. Examples of natural SDPs are the proteins and nucleic acids that possess the structural and functional complexity to support life. Highly sophisticated machinery has evolved in living organisms for the de novo synthesis of natural SDPs. However, gaining absolute control of the monomer sequence in a non-natural polymer is still challenging. In comparison to biopolymers, non-natural SDPs have an even wider scope of unlimited functional side-chains, as well as backbone diversity. Hence, SDP is a perfect platform for generating extensive structural complexity such as self-assembly into nanostructures, folding, the formation of stimuli-responsive sites, catalytic sites, and so on. In this review, the current status of the SDPs that have tremendous potential for future research and development are discussed. This review seeks to draw attention to the development of non-natural SDPs via innovative synthetic routes established recently. After synthesis and characterization, the next obvious step to move the field forward is to explore SDPs for their potential applications. Hence, this review is divided into two parts: (i) diversified synthetic strategies for SDPs, and (ii) applications of SDPs in materials and biomedical sciences. This field is progressing rapidly; there are immense possibilities for exploring different chemical reactions to develop novel classes of SDPs, and there are many potential application opportunities via pre-determined sequences in synthetic polymers. © The Royal Society of Chemistry.