The concept of probability (or chance) and probabilistic analyses play a central role in almost all modern sciences, often in theoretical as well as experimental or observational contexts. So it is a curious fact that there is no more basic agreement on what probabilities are (what probability claims mean, their truth conditions, how they can be tested, and so forth) now than there was 50 or 100 years ago. We will study the subjectivist approach to probability, frequentism, and propensity analyses, to get an overview of their strengths and weaknesses and how well they accord with our intuitions and our uses of probability. Recent work on Humean theories of objective chance, by Lewis and others, will be covered in depth. We will examine how philosophers try to use probability and chance in their accounts of knowledge, explanation, causation, laws of nature and other topics, and examine whether the desiderata of philosophers on the one hand, and working scientists on the other, can be jointly satisfied.