Distributed consensus in the Wasserstein metric space of probability measures was the primary topic of investigation under this project. Convergence of each agent's (or nodes) measure to a common probability measure is proven under a weak networkconnectivity condition. The common measure reached at each agent is one minimizing a weighted sum of its Wasserstein distance to all initial agent measures. This measure is known as the Wasserstein barycenter. Special cases involving Gaussian measures,empirical measures, and time-invariant network topologies are considered, where convergence rates and average-consensus results are given. This algorithm has potential applicability in computer vision, machine learning and distributed estimation, etc. Anumber of other topics in distributed and Monte-Carlo estimation were also considered including: distributed information fusion under unknown correlations; large-scale sequential Monte-Carlo methods; optimal controller approximation via Monte-Carlomethods; score and information matrix approximation via sequential Monte-Carlo methods.