Federated learning (FL) is a trending framework to enable multi-institutional collaboration in machine learning without sharing raw data. This presentation will discuss our ongoing progress in designing FL algorithms that embrace the data heterogeneity properties for distributed medical data analysis in the FL setting. First, I will present our work on theoretically understanding FL training convergence and generalization using a neural tangent kernel, called FL-NTK. Then, I will present our algorithms for tackling data heterogeneity (on features and labels) and device heterogeneity, motivated by our previous theoretical foundation. Lastly, I will also show the promising results of applying our FL algorithms in healthcare applications.