PyTorch-Kaldi is an open-source toolkit for building state-of-the-art DNN/RNN hybrid speech recognition systems. The project integrates PyTorch for managing deep neural network components (DNN, RNN, LSTM, GRU) with the Kaldi toolkit for feature extraction, label computation, and decoding. It implements the DNN-HMM hybrid approach common in ASR systems, where neural networks provide acoustic predictions that feed into a hidden Markov model decoder. The toolkit aims to improve transparency and replicability of speech recognition research.