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Our group is applying the techniques of modern atomic physics to the system of diatomic molecules. Molecules are more complex than atoms because of their vibrational and rotational degrees of freedom, and this makes them difficult to control. However, we have identified a variety of simple principles that allow us to make use of these "new" properties to provide powerful types of leverage on a broad range of problems. These span fields all the way from particle physics to quantum computation to chemical physics. This talk will give an overview of the field, along with some specific examples of our recent work. These include the first-ever laser cooling of a molecule, and the search for the CP-violating electric dipole moment of the electron.