Explore the semantic foundations of probabilistic and statistical modelling in this comprehensive tutorial from TutorialFest at POPL'24. Delve into the use of types to introduce, utilize, and organize abstractions for probabilistic modelling, starting with discrete probability and progressing to the recently-developed quasi-Borel spaces. Gain hands-on experience through accompanying exercises for self-study, allowing you to develop a working knowledge of the subject matter. Led by Ohad Kammar, this 1 hour and 55 minute session offers a deep dive into the latest breakthroughs in the field, providing valuable insights for researchers and practitioners in probabilistic programming and type theory.