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Speech communication using the Voice over Internet Protocol (VoIP) is very common today. The underlying network channel may be the public switched telephone network (PSTN channel), satellite channels or cellular wireless channels to name a few. The packetization of speech and its transmission through packet switched networks, however, introduce numerous impairments such as delay, jitter, packet loss and decoder clock offset, which degrade the quality of the speech. We present an overview of the challenges and a description of the advanced signal processing algorithms used to combat these impairments and render the perceived quality of a VoIP conversation to be as good as that of the existing telephone system. We also present an example of a speech coder designed for packet-switched networks and discuss the possibilities for hardware implementations.