In this dissertation, the feedback whistling problem with digital hearing instruments is investigated. The work focuses on the properties of the feedback path, the modelling of the feedback path and the feedback suppression techniques. The properties and modelling of the feedback path are first discussed. Along the propagation path, different components compose the feedback path. The effects of these components are analyzed and categorized. Accordingly an ideal feedback path model, which consists of a fixed model, a slowing varying model and a fast varying model, is suggested in the dissertation. Methods to extract the fixed model are proposed and proved to be effective in representing the invariant part of the feedback path. Based on the investigation of the dynamic changes of the feedback path in adverse situations, for example when the user picks up the telephone handset, a reflection model is developed as one type of the fast varying models. The techniques to suppress the feedback are then reviewed. To improve the existing feedback suppression systems, two approaches are proposed to address the so-called “bias problem”. The first approach improves the performance of the adaptive feedback canceller with filtered-X adaptation by injecting nearly inaudible noise. The second approach uses a linear predicative coding based vocoder to synthesize the hearing-aid output in order to decorrelate the hearing-aid output signal and the desired input signal. In the end, a discussion about the use of the proposed feedback path models in the feedback cancellation systems is presented.