Neural codecs have become crucial to recent speech and audio generation research. In addition to signal compression capabilities, discrete codecs have also been found to enhance downstream training efficiency and compatibility with autoregressive language models. However, as extensive downstream applications are investigated, challenges have arisen in ensuring fair comparisons across diverse applications. To address these issues, we present a new open-source platform ESPnet-Codec, which is built on ESPnet and focuses on neural codec training and evaluation. ESPnet-Codec offers various recipes in audio, music, and speech for training and evaluation using several widely adopted codec models. Together with ESPnet-Codec, we present VERSA, a standalone evaluation toolkit, which provides a comprehensive evaluation of codec performance over 20 audio evaluation metrics. Notably, we demonstrate that ESPnet-Codec can be integrated into six ESPnet tasks, supporting diverse applications.