Federated Learning (FL) is a distributed learning paradigm where clients collaboratively train a model while keeping their own data private. With an increasing scale of clients and models, FL encounters two key challenges, client drift due to a high degree of statistical/system heterogeneity, and lack of adaptivity. However, most existing FL research is based on unrealistic assumptions that virtually ignore system heterogeneity. In this paper, we propose Client-Centric Federated Adaptive Optimization, which is a class of novel federated adaptive optimization approaches. We enable several features in this framework such as arbitrary client participation, asynchronous server aggregation, and heterogeneous local computing, which are ubiquitous in real-world FL systems but are missed in most existing works. We provide a rigorous convergence analysis of our proposed framework for general nonconvex objectives, which is shown to converge with the best-known rate. Extensive experiments show that our approaches consistently outperform the baseline by a large margin across benchmarks.