Analogical reasoning, the ability to map different domains using their structural similarity, is a core mechanism of human cognition that supports tasks such as problem-solving, argumentation, and creativity. Despite recent advances in AI systems, including Large Language Models (LLMs), they still struggle to perform analogical reasoning reliably. In this project, we get inspiration by cognitive theories of analogy and try to develop models that can better capture and perform analogical reasoning. As a key component, we investigate abstraction levels and study how to best extract and represent them. In addition, we systematically analyze the limitations of LLMs by developing a dataset annotated with analogical structure and explore fine-tuning approaches to improve their analogical reasoning abilities.