 Stalnaker’s Thesis is consistent for simple conditionals, but fails for conditionals of arbitrary complexity. A challenge is to extend Stalnaker’s Thesis to more or less extended classes of compound conditionals. Several proposals have been made toward that goal. The associated literature is quite technical, however, and we give only a few landmarks here. Important is that all the resulting systems mentioned here conservatively extend Adams’s basic logic, namely system P (i.e., they preserve the same axioms for simple conditionals, though not necessarily for compound conditionals).