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Statistical analysis based on random fields has become a widely used approach in order to better understand real processes in many fields such as engineering, environmental sciences, etc. Data analysis based on random fields can be sometimes problematic to carry out from the inferential prospective. Examples are when dealing with: large dataset, counts or binary responses and extreme values data. This article explains how to perform, with the R package CompRandFld, challenging statistical analysis based on Gaussian, binary and max-stable random fields. The software provides tools for performing the statistical inference based on the composite likelihood in complex problems where standard likelihood methods are difficult to apply. The principal features are illustrated by means of simulation examples and an application of Irish daily wind speeds.