Ever since the Standard Model (SM) has been written down, countless efforts have been made to complement/extend it with new inputs from both theoretical and experimental sides. In this work, we provide such possible extensions from two perspectives: phenomenology (model-building) and data analysis. From the model-building perspective, dark matter has proven to be one of the most robust signs we have about new physics. As such, we propose new models involving dark matter, along with analyses of their properties and methods of probing them in experiments. An alternative approach of discovering new physics involves the use of more sophisticated data analysis methods based on modern machine learning models and techniques. On this front, we present works regarding improvements towards two existing proposals - 'Classification Without Labels' and 'Anomaly Detection with Density Estimation'.