In this talk on a more classical part of ergodic theory, that of Z-actions, I will explain the construction of rank-one transformations via cutting and stacking that goes back to von Neumann and Kakutani and has been used to create examples and counterexamples of various mixing-like properties. Following the explanation of the subject, I will present some of my work on when such transformations are mixing. Some of the results presented are joint work with Cesar Silva.