1. INTRODUCTION Driven by the continuous progress in the semiconductor technology, today’s high-end digital hearing aids offer powerful digital signal processing on which this paper focuses. Figure 1 schematically shows the main signal processing blocks of a high-end hearing aid [1]. In this paper, we will follow the depicted signal flow and discuss the state of the art, the challenges, and future trends for the different components. A coarse overview is given below. First,theacousticsignaliscapturedbyuptothreemicrophones. The microphone signals are processed into a single signal within the directional microphone unit which will be discussed in Section 2. The obtained monosignal is further processed separately for different frequency ranges. In general, this requires an analysis filterbank and a corresponding signal synthesis. The main frequency-band-dependent processing steps are noise reduction as detailed in Section 3 and signal amplification combined with dynamic compression as discussed in Section 4. A technically challenging problem of hearing aids is the risk of acoustic feedback that is provoked by strong signal amplificationincombinationwithmicrophonesandreceiver