Parallel computing in Gaussian process calculations becomes necessary for avoiding computational and memory restrictions associated with large-scale environmental data science applications. The evaluation of the Gaussian log-likelihood function requires O(n^2) storage and O(n^3) operations where n is the number of geographical locations. Thus, computing the log-likelihood function with a large number of locations requires exploiting the power of existing parallel computing hardware systems, such as shared-memory, possibly equipped with GPUs, and distributed-memory systems, to solve this computational complexity. In this paper, we advocate the use of ExaGeoStatR, a package for exascale Geostatistics in R that supports a parallel computation of the exact maximum likelihood function on a wide variety of parallel architectures. Parallelization in ExaGeoStatR depends on breaking down the numerical linear algebra operations in the log-likelihood function into a set of tasks and rendering them for a task-based programming model. The package can be used directly through the R environment on parallel systems. Currently, ExaGeoStatR supports several maximum likelihood computation variants such as exact, Diagonal Super Tile (DST), Tile Low-Rank (TLR) approximations, and Mixed-Precision (MP). ExaGeoStatR also provides a tool to simulate large-scale synthetic datasets. These datasets can help to assess different implementations of the maximum log-likelihood approximation methods. Here, we demonstrate ExaGeoStatR by illustrating its implementation details, analyzing its performance on various parallel architectures, and assessing its accuracy using synthetic datasets with up to 250K observations. We provide a hands-on tutorial to analyze a sea surface temperature real dataset. The performance evaluation involves comparisons with the popular packages geoR and fields for exact likelihood evaluation.