Robust ASR refers to the research field that addresses such performance degradation. Conventionally, the robustness of ASR models to background noise is improved by cascading speech separation and enhancement frontends and ASR backends. Speech separation refers to the case where the background is highly non-stationary and can contain difficult sources such as music or other speech signals. This problem has traditionally been addressed using model-based approaches, for example based on hidden Markov models (HMMs), or non-negative matrix factorization (NMF). More recently, however, various data-driven discriminative approaches, relying on deep learning techniques are proved to be effective for this task. Therefore, the objective of this project is to develop the machine learning and signal processing tools and techniques that can be used to improve the accuracy of monaural ASR systems in adverse real-world scenarios. To achieve this, we draw upon the recent theoretical advances in the field of data driven speech separation techniques in both time-domain and frequency-domain using deep neural networks.