Learning techniques are drawing extensive attention in the robotics community. Some reasons behind moving from traditional preprogrammed robots to more advanced human fashioned techniques are to save time and energy, and allow non-technical users to easily work with robots. Learning from Demonstration (LfD) and Imitation Learning (IL) are among the most popular learning techniques to teach robots new skills by observing a human or robot tutor. Flawlessly teaching robots new skills by LfD requires good understanding of all challenges in the field. Studies of imitation learning in humans and animals show that several cognitive abilities are engaged to correctly learn new skills. The most remarkable ones are the ability to direct attention to important aspects of demonstrations, and adapting observed actions to the agents own body. Moreover, a clear understanding of the demonstrator's intentions is essential for correctly and completely replicating the behavior with the same effects on the world. Once learning is accomplished, various stimuli may trigger the cognitive system to execute new skills that have become part of the repertoire. Considering identified main challenges, the current thesis attempts to model imitation learning in robots, mainly focusing on understanding the tutor's intentions and recognizing what elements of the demonstration need the robot's attention. Thereby, an architecture containing required cognitive functions for learning and reproducing high-level aspects of demonstrations is proposed. Several learning methods for directing the robot's attention and identifying relevant information are introduced. The architecture integrates motor actions with concepts, objects and environmental states to ensure correct reproduction of skills. This is further applied in learning object affordances, behavior arbitration and goal emulation. The architecture and learning methods are applied and evaluated in several real world scenarios that require clear understanding of goals and what to look for in the demonstrations. Finally, the developed learning methods are compared, and conditions where each of them has better applicability is specified.