The analysis of ocean and atmospheric datasets offers a unique set of challenges to scientists working in different application areas. These challenges include dealing with extremely large volumes of multidimensional data, supporting interactive visual analysis, ensembles exploration and visualization, exploring model sensitivities to inputs, mesoscale ocean features analysis, predictive analytics, heterogeneity and complexity of observational data, representing uncertainty, and many more. Researchers across disciplines collaborate to address such challenges, which led to significant research and development advances in ocean and atmospheric sciences, and also in several relevant areas such as visualization and visual analytics, big data analytics, machine learning and statistics. In this report, we perform an extensive survey of research advances in the visual analysis of ocean and atmospheric datasets. First, we survey the task requirements by conducting interviews with researchers, domain experts, and end users working with these datasets on a spectrum of analytics problems in the domain of ocean and atmospheric sciences. We then discuss existing models and frameworks related to data analysis, sense-making, and knowledge discovery for visual analytics applications. We categorize the techniques, systems, and tools presented in the literature based on the taxonomies of task requirements, interaction methods, visualization techniques, machine learning and statistical methods, evaluation methods, data types, data dimensions and size, spatial scale and application areas. We then evaluate the task requirements identified based on our interviews with domain experts in the context of categorized research based on our taxonomies, and existing models and frameworks of visual analytics to determine the extent to which they fulfill these task requirements, and identify the gaps in current research. In the last part of this report, we summarize the trends, challenges, and opportunities for future research in this area. (see http://www.acm.org/about/class/class/2012).