Robust source decoding algorithms are required in digital communications when signals are transmitted over error-prone channels. This is due to the fact that even single residual bit errors after a possible error correction scheme can lead to annoying distortions. In addition, a considerable amount of redundancy is available even in efficiently source-coded signals (e.g., DVB-T or DAB+ data streams). Therefore, it is reasonable to employ robust source-decoding algorithms next to classical channel coding schemes in order to exploit this redundancy. This research focuses on robust speech and audio decoding algorithms with no or low algorithmic delay and with or without explicit redundancy schemes. Our algorithms can be employed in a wide range of audio applications such as digital wireless microphones, digital wireless headphones or receivers for digital radio (e.g., DAB, DAB+).