Hydrogen is an important impurity in zinc oxide and can be incorporated into the lattice in several ways. Hydrogen can be also bound by vacancies that can be studied using positron annihilation techniques. Here we examine theoretically oxygen and zinc vacancies in ZnO, the latter also with hydrogen atoms inside. Several computational approaches are employed to determine the defect geometries and related positron characteristics. Positron-induced forces are also taken into account. Calculated positron lifetimes are compared with those observed in experiment, which gives an indication of the presence of zinc vacancy-hydrogen complexes in ZnO materials.