Title: One Ring to Bring Them All: Model Adaptation under Domain and Category Shift. Abstract: In this paper, we investigate model adaptation under domain and category shift, where the final goal is to achieve $\textit{Source-free Universal Domain Adaptation}$ (SF-UNDA), which addresses the situation where there exist both domain and category shifts between source and target domains. Under the SF-UNDA setting, the model cannot access source data anymore during target adaptation, which aims to address data privacy concerns. We propose a novel training scheme to learn a ($n$+1)-way classifier to predict the $n$ source classes and the unknown class, where samples of only known source categories are available for training. Furthermore, for target adaptation, we simply adopt a weighted entropy minimization to adapt the source pretrained model to the unlabeled target domain without source data. In experiments, we show: $\textbf{1)}$ After source training, the resulting source model can get excellent performance for $\textit{open-set single domain generalization}$; $\textbf{2)}$ After target adaptation, our method surpasses current UNDA approaches which demand source data during adaptation. The versatility to several different tasks strongly proves the efficacy and generalization ability of our method. $\textbf{3)}$ When augmented with a closed-set domain adaptation approach during target adaptation, our source-free method further outperforms the current state-of-the-art UNDA method by 2.5%, 7.2% and 13% on Office-31, Office-Home and VisDA respectively.