Growth of MgB2thin films by pulsed laser deposition is examined under ex situ and in situprocessing conditions. For the ex situ process, boronfilmsgrown by pulsed laser deposition were annealed at 900 °C with excess Mg. For the in situ process, different approaches involving ablation from a stoichiometric target under different growth conditions, as well as multilayer deposition involving interposed Mg layers were examined and analyzed. Magnetic measurements on ex situ processed films show Tc of ∼39 K, while the current best in situfilms show a susceptibility transition at ∼22 K.