Meta-analyses are essential for cumulative science, but their validity can be compromised by publication bias. To mitigate the impact of publication bias, one may apply publication-bias-adjustment techniques such as precision-effect test and precision-effect estimate with standard errors (PET-PEESE) and selection models. These methods, implemented in JASP and R, allow researchers without programming experience to conduct state-of-the-art publication-bias-adjusted meta-analysis. In this tutorial, we demonstrate how to conduct a publication-bias-adjusted meta-analysis in JASP and R and interpret the results. First, we explain two frequentist bias-correction methods: PET-PEESE and selection models. Second, we introduce robust Bayesian meta-analysis, a Bayesian approach that simultaneously considers both PET-PEESE and selection models. We illustrate the methodology on an example data set, provide an instructional video ( https://bit.ly/pubbias ) and an R-markdown script ( https://osf.io/uhaew/ ), and discuss the interpretation of the results. Finally, we include concrete guidance on reporting the meta-analytic results in an academic article.