An overview is given over a fair range of topics within spatial and sp
atial-temporal statistics. The theory presented is motivated by and il
lustrated with actual applications to real world problems. We describe
and discuss models for three basic types of spatial processes: contin
uous random surfaces, mosaic phenomena, and events-against-background
processes. Various combinations of these sometimes occur naturally in
applications, like Gaussian noise on top of a Markov random field in i
mage restoration problems, Some of these combinations are also discuss
ed, The applications we discuss are drawn from the areas of medical im
age analysis, pollution monitoring, characterisation of oil reservoirs
, estimation of fish and whale stock, forestry surveillance via satell
ite, statistical meteorology, and symbol recognition,