A defining trait of federated learning is the presence of heterogeneity, i.e., that data may differ significantly across the network. In this talk I discuss how heterogeneity affects issues of fairness and robustness in federated settings. Our work demonstrates that robustness to data/model poisoning attacks and fairness, measured as the uniformity of performance across devices, are constraints that can directly compete when training in heterogeneous networks. I then explore to what extent methods for personalized federated learning can mitigate the tension between these constraints. I end with promising directions of future work in personalization, fairness, and robustness for FL.