In this talk, we discuss distributionally robust geometric programs with individual and joint chance constraints. We consider three groups of uncertainty sets, namely uncertainty sets with known two first order moments information, uncertainty sets considering the uncertainties in terms of the distribution and the moments, and uncertainty sets constrained by the Kullback-Leibler divergence distance with a normal reference distribution. We present tractable reformulations for geometric programs with individual chance constraints for the three uncertainty sets. Efficient approximations are given for distributionally robust programs with joint chance constraints using piecewise linear functions. Numerical results are given on a shape optimization problem.