Since the first reports of their successful synthesis in 2015, all-inorganic perovskite quantum dots (PQDs), emerged as promising material for lighting applications. Despite their unique optical properties, to date, PQDs based LEDs and lasing media operation is still far from ideal. One of the limiting factors is the strong Coulomb interaction, which contributes to nonradiative decay processes. Here, we discuss in detail the multiexciton interactions in PQDs based on their size dependence. We expand on their nonlinear optical properties, focusing on the two-photon absorption characteristics, showing results for two-photon pumped amplified stimulated emission, suggesting that these materials may be promising for two-photon pumped lasers.