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Towards realtime mapping, we develop a framework in which spatially varying hyperparameters of the Gaussian process kernel can be trained online while remaining computationally manageable, and demonstrate the advantage of our method in accurately mapping spatial phenomena with changing local variability. In decentralized settings, we propose a communication criteria that maximizes mutual information to facilitate collaborative multi-agent mapping in low communication bandwidth environments. Simulation experiments explore the trade-off between model similarity and joint information gain. Next, we examine the environmental monitoring problem in the Bayesian optimization framework. We propose a Gaussian process pure exploration algorithm with easily computable theoretical bounds on the simple regret, that delineate the relationship between number of samples and solution accuracy. 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Simulation experiments explore the trade-off between model similarity and joint information gain. Next, we examine the environmental monitoring problem in the Bayesian optimization framework. We propose a Gaussian process pure exploration algorithm with easily computable theoretical bounds on the simple regret, that delineate the relationship between number of samples and solution accuracy. 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