Title: Practical and Private Heterogeneous Federated Learning. Abstract: Heterogeneous federated learning (HFL) enables clients with different computation/communication capabilities to collaboratively train their own customized models, in which the knowledge of models is shared via clients' predictions on a public dataset. However, there are two major limitations: 1) The assumption of public datasets may be unrealistic for data-critical scenarios such as Healthcare and Finance. 2) HFL is vulnerable to various privacy violations since the samples and predictions are completely exposed to adversaries. In this work, we develop PrivHFL, a general and practical framework for privacy-preserving HFL. We bypass the limitations of public datasets by designing a simple yet effective dataset expansion method. The main insight is that expanded data could provide good coverage of natural distributions, which is conducive to the sharing of model knowledge. To further tackle the privacy issue, we exploit the lightweight additive secret sharing technique to construct a series of tailored cryptographic protocols for key building blocks such as secure prediction. Our protocols implement ciphertext operations through simple vectorized computations, which are friendly with GPUs and can be processed by highly-optimized CUDA kernels. Extensive evaluations demonstrate that PrivHFL outperforms prior art up to two orders of magnitude in efficiency and realizes significant accuracy gains on top of the stand-alone method.