A helical structure is a collection of molecules at positions given by the orbit of a helical group acting on the position vectors of the atoms of a single molecule. In this thesis, we systematically study phase transformations from one helical structure to another and search for potential applications. Motivated in part by recent work that relates the presence of compatible interfaces with properties such as the hysteresis and reversibility of a phase transformation, we give necessary and sufficient conditions on the structural parameters of two helical phases such that they are compatible. We show that, locally, four types of compatible interfaces are possible: vertical, horizontal, helical and elliptical. Furthermore, we discuss more complex microstructures in transforming helical structures that mix different types of these interfaces. Similar to crystal case, we conjecture that compatible helical transformations with low hysteresis and fatigue resistance would exhibit an unusual shape memory effect involving both twist and extension.