This talk proposes a general gradient normalization technique that can be readily applied to numerous popular distributed learning algorithms such as compressed distributed stochastic gradient descent, federated averaging, and asynchronous distributed stochastic gradient descent. Through rigorous analysis, we prove gradient normalization removes the adverse influence of data heterogeneity on all these algorithms and enables them to achieve linear speedup rates without assuming any bounded data heterogeneity. Numerical experiments are conducted to validate all theoretical findings.