In this talk, we will present algorithms for distributed statistical estimation that can take advantage of the divide-and-conquer approach. We show that one of the key benefits attained by an appropriate divide-and-conquer strategy is robustness, an important characteristic of large distributed systems. Moreover, we introduce a class of algorithms that are based on the properties of the spatial median, establish connections between performance of these distributed algorithms and rates of convergence in normal approximation, and provide tight deviations guarantees for resulting estimators in the form of exponential concentration inequalities. Techniques are illustrated with several examples; in particular, we obtain new results for the median-of-means estimator, as well as provide performance guarantees for robust distributed maximum likelihood estimation.