Abstract: I plan to talk on several loosely related different contributions I have made in the area known as free function theory or noncommutative function theory. In fact, I will consider only polynomials, power series, or rational functions in noncommuting d-variables. The goal is to show that in the noncommutative setting things often work as well as in the commutative, single-variable case, while the commutative d-variable analogues are more complicated. Moreover, in some circumstances the noncommutative results can be applied to obtain corresponding statements in the commutative setting via a "noncommutative lifting" that I will describe.