In the basic communication complexity model, two or more players aim to compute a joint function, with each player privately holding a portion of the input. Assuming unlimited individual computational power, their common goal is to determine the function’s value while exchanging as little information as possible. Though seemingly unrealistic, communication complexity has proven highly useful for establishing impossibility results across many areas of computer science, both theoretical and applied. 
In this talk, I will survey several results from my past research in communication complexity, highlighting applications to algorithm design and learning theory. I will illustrate how communication complexity techniques yield provable hardness results, providing insights into the fundamental limits of computational tasks and guiding the design of efficient algorithms.