Deep learning has significantly improved the state of the art for several tasks in computer vision and robotic perception. However, a major obstacle in adopting deep models in real world applications is the fact that their performances significantly drop when there is a shift in data distributions across training and test data. Furthermore, deep networks are known to suffer from catastrophic forgetting when we want to incorporate novel information as new data becomes available. These problems have motivated research into domain adaptation (DA) and continual learning (CL). While in the last few years several efforts have been made to develop DA and CL methods, still few approaches have explicitly focused on devising deep adaptive neural networks that can operate in a resource constrained regime (low memory/computational resources). This will be of utmost importance in many applications, e.g. robotics perception. The aim of the PhD is to study and develop novel algorithms for domain adaptation/generalization and continual learning with special emphasis on deep architectures which can be deployed in resource constrained settings.