In this paper, signal processing techniques for environmental noise reduction and howling suppression, which have mainly been developed for other applications but are also applicable to hearing aids, are discussed. Among noise reduction techniques, adaptive signal processing including the adaptive beamformer and speech spectrum/parameter estimator is discussed. Especially, in the adaptive beamformer, an effort to reduce impulsive noise, which severely reduces intelligibility in daily communication but is difficult to deal with by conventional adaptive schemes, is described. In howling suppression, two approaches, i.e., the adaptive feedback canceler and the adaptive notch filter, are discussed.