Poly(organo)phosphazenes are a family of inorganic molecular hybrid polymers with very diverse properties due to the vast array of organic substituents possible. This tutorial review aims to introduce the basics of the synthetic chemistry of polyphosphazenes, detailing for readers outside the field the essential knowledge required to design and prepare polyphosphazenes with desired properties. A particular focus is given to some of the recent advances in their chemical synthesis which allows not only the preparation of polyphosphazenes with controlled molecular weights and polydispersities, but also novel branched architectures and block copolymers. We also discuss the preparation of supramolecular structures, bioconjugates and in situ forming gels from this diverse family of functional materials. This tutorial review aims to equip the reader to prepare defined polyphosphazenes with unique property combinations and in doing so we hope to stimulate further research and yet more innovative applications for these highly interesting multifaceted materials.