We present the task description and discussion on the results of the DCASE 2021 Challenge Task 2. Last year, we organized unsupervised anomalous sound detection (ASD) task; identifying whether the given sound is normal or anomalous without anomalous training data. In this year, we organize an advanced unsupervised ASD task under domain-shift conditions which focuses on the inevitable problem for the practical use of ASD systems. The main challenge of this task is to detect unknown anomalous sounds where the acoustic characteristics of the training and testing samples are different, i.e. domain-shifted. This problem is frequently occurs due to changes in seasons, manufactured products, and/or environmental noise. After the challenge submission deadline, we will add challenge results and analysis of the submissions.