Gamma-positivity is a property of polynomials that implies palindromicity and unimodality. It has received considerable attention in recent times because of Gal's conjecture, which asserts gamma-positivity of the h-polynomial of flag homology spheres. The Eulerian polynomials and the Narayana polynomials are examples of such h-polynomials that are known to be gamma-positive. In this talk I will present q-analogs of formulas establishing gamma-positivity of these and other polynomials. Geometric interpretations involving toric varieties and consequences such as q-unimodality will also be discussed. This is based on joint work with John Shareshian and with Christian Krattenthaler.