The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein. Topological Deep Learning (TDL) provides a framework to process and extract knowledge from data associated with these systems, such as predicting the social community to which an individual belongs or predicting whether a protein can be a reasonable target for drug development. By extending beyond traditional graph-based methods, TDL incorporates higher-order relational structures, providing a new lens to tackle challenges in applied sciences and beyond. This talk will introduce the core principles of TDL and provide a comprehensive review of its rapidly growing literature, with a particular focus on neural network architectures and their performance across various domains. I will present open-source implementations that make TDL methods more accessible and practical for real-world applications. All in all, this talk will showcase how TDL models can effectively capture and reason about the complexity of real-world systems, while highlighting the remaining challenges and exciting opportunities for future advancements in the field.