We provide a discussion of several recent results which, in certain scenarios, are able to overcome a barrier in distributed stochastic optimization for machine learning. Our focus is the so-called asymptotic network independence property, which is achieved whenever a distributed method executed over a network of n nodes asymptotically converges to the optimal solution at a comparable rate to a centralized method with the same computational power as the entire network. We explain this property through an example involving the training of ML models and sketch a short mathematical analysis for comparing the performance of distributed stochastic gradient descent (DSGD) with centralized stochastic gradient decent (SGD).