In the progression of physics, most facts and laws have been established only after decades, often centuries, of discussion and dispute. This conference will review some of the great disputes stretching from antiquity to the modern day. From the classical Greek discussions on the nature of space and matter, through the founding disputes of modern science and its mathematics (led by Newton's disputes with contemporaries) up to the recent controversies in quantum mechanics and cosmology, the feuds between leading thinkers and their vital role in establishing successive views of our physical world will be examined.