A very important factor for the commercial success of mobile phones, speech dialog systems, and teleconferencing equipment is the high quality of the handsfree voice interface. Unfortunately, we observe that many of the existing solutions still exhibit severe quality deficiencies, e.g., in the form of acoustic talker echo, half-duplex ability, or unnatural background noise transmission. In order to combat these problems, a new model-based adaptive filtering approach is pursued in this work, taking fundamental physical properties of realistic acoustic environments into account, e.g., acoustic echo path variability, infinite reverberation, and ambient noise characteristics. Since an appropriate physical model for the time-varying echo path does not exist in literature, a stochastic state-space model is proposed here. Based on the model, a two-stage adaptive filter structure is derived for estimating the desired speech signal from the disturbed microphone signal in the minimum mean-square error sense. The key to the analytic derivation and accurate approximation of adaptive algorithms is the adequate treatment of statistical Kalman filtering in the frequency domain. It turns out that the model-based approach leads to an outstandingly compact and robust signal processing solution for acoustic echo control. This technique no longer requires the traditional control mechanisms, e.g., double talk detection or echo path change detection, in order to achieve stability and high-end performance in realistic acoustic environments. Thus, the proposed concept is suitable for direct and efficient implementation in today's and tomorrow's voice communication systems. It is explained how these properties were confirmed by a realtime prototype system that has been evaluated in different realworld applications.