  Environmental and climate processes are often distributed over large
space-time domains. Their complexity and the amount of available data make
modelling and analysis a challenging task. Statistical modelling of environment
and climate data can have several different motivations including
interpretation or characterisation of the data. Results from statistical
analysis are often used as a integral part of larger environmental studies.
Spatial statistics is an active and modern statistical field, concerned with
the quantitative analysis of spatial data; their dependencies and
uncertainties. Spatio-temporal statistics extends spatial statistics through
the addition of time to the, two or three, spatial dimensions. The focus of
this introductory paper is to provide an overview of spatial methods and their
application to environmental and climate data. This paper also gives an
overview of several important topics including large data sets and
non-stationary covariance structures. Further, it is discussed how Bayesian
hierarchical models can provide a flexible way of constructing models.
Hierarchical models may seem to be a good solution, but they have challenges of
their own such as, parameter estimation. Finally, the application of
spatio-temporal models to the LANDCLIM data (LAND cover - CLIMate interactions
in NW Europe during the Holocene) will be discussed.
