The efficiency of thermoelectric devices for converting waste heat into useful electrical energy depends on the figure of merit ZT. The numerator in the ZT expression is called the power factor, which is proportional to the square of the Seebeck coefficient and to the electrical conductance, and its denominator is the thermal conductance. Therefore, thermoelectric materials should simultaneously have a high Seebeck coefficient, a high electrical conductance, and a low thermal conductance. Graphene, a recently discovered form of carbon, has received significant attention over the last few years due to its excellent electrical, optical, and thermal properties. Graphene, however, is not a useful thermoelectric material. Although its electrical conductance is as high as that of copper, its ability to conduct heat is even higher, which increases the denominator of ZT. Furthermore, as a zero bandgap material, pristine graphene has a very small Seebeck coefficient, which minimizes the power factor. Nanoengineering, however, provides simultaneous ways to increase the Seebeck coefficient and decrease the thermal conductivity as well. We have conducted a comprehensive theoretical study on thermoelectric properties of graphene antidot lattices. In order to improve the Seebeck coefficient graphene needs to acquire a bandgap. Using an atomistic tight-binding model, the electronic structure of graphene antidot lattices was calculated. Our results indicate that a direct bandgap can be achieved by properly engineering the geometrical properties of the antidots introduced in the graphene. For the phononic structure we used a fourth nearest neighbor force constant method. The phononic band structure is in good agreement with the experimental results, as shown in the figure. We showed that by introducing antidots in the graphene sheet, some phonon modes became localized and did not contribute to the thermal conductance. As a result, the thermal conductivity of graphene antidot lattices decreased and the respective ZT value increased.