In this work, recent progress in the theoretical and experimental studies of optical-fiber microcoil waveguides and resonators, as well as their various applications are reviewed. In particular, the focus is set on sensing and interferometry applications. It is shown that due to its inherently low propagation and fiber-coupling losses, fiber-microcoil based sensors and interferometers offer substantial enhancement of sensitivity and compactness compared to other types of devices. Recent progress in the realization and experimental characterization of such structures is presented and the theoretical tools to analyze the impact of real-world nonuniformities on the characteristics of fiber-microcoil structures are provided.