We present an analysis of positron lifetimes in solids with unprecedented depth. Instead of modeling correlation effects with density functionals, we study positron-electron wave functions with long-range correlations included. This gives new insight in understanding positron annihilation in metals, insulators, and semiconductors. By using a new quantum Monte Carlo approach for computation of positron lifetimes, an improved accuracy compared to previous computations is obtained for a representative set of materials when compared with experiment. Thus, we present a method without free parameters as a useful alternative to the already existing methods for modeling positrons in solids.