Archaeologists often use data and quantitative statistical methods to evaluate their ideas. Although thereare various statistical frameworks for decision-making in archaeology and science in general, in this chapter,we provide a simple explanation of Bayesian statistics. To contextualize the Bayesian statistical framework,we briefly compare it to the more widespread null hypothesis significance testing (NHST) approach. Wealso provide a simple example to illustrate how archaeologists use data and the Bayesian framework to com-pare hypotheses and evaluate their uncertainty. We then review how archaeologists have applied Bayesianstatistics to solve research problems related to radiocarbon dating and chronology, lithic, ceramic, zooarchae-ological, bioarchaeological, and spatial analyses. Because recent work has reviewed Bayesian applications inarchaeology from the 1990s up to 2017 (Caitlin E. Buck, Cavanagh, and Litton 1996; Caitlin E. Buck 2001;Otárola-Castillo and Torquato 2018), this work considers the relevant literature published since 2017.