Noise is ubiquitous in almost all acoustic environments. The speech signal, that is recorded by a microphone is generally infected by noise originating from various sources. Such contamination can change the characteristics of the speech signals and degrade the speech quality and intelligibility, thereby causing significant harm to human-to-machine communication systems. Noise detection and reduction for speech applications is often formulated as a digital filtering problem, where the clean speech estimation is obtained by passing the noisy speech through a linear filter. With such a formulation, the core issue of noise reduction becomes how to design an optimal filter that can significantly suppress noise without noticeable speech distortion. This paper focuses on voice activity detection, noise estimation, removal techniques and an optimal filter.