We adaptively estimate both changepoints and local outlier processes in a Bayesian dynamic linear model with global-local shrinkage priors in a novel model we call Adaptive Bayesian Changepoints with Outliers (ABCO). We utilize a state-space approach to identify a dynamic signal in the presence of outliers and measurement error with stochastic volatility. We find that global state equation parameters are inadequate for most real applications and we include local parameters to track noise at each time-step. This setup provides a flexible framework to detect unspecified changepoints in complex series, such as those with large interruptions in local trends, with robustness to outliers and heteroskedastic noise. Finally, we compare our algorithm against several alternatives to demonstrate its efficacy in diverse simulation scenarios and two empirical examples on the U.S. economy.