Random Spatial Processes, in particular Percolation, Interacting Particle Systems and Gibbs Measures, has become one of the most active subfields of modern Probability. Motivated by problems in Physics (phase transitions), Biology (epidemics) and, more recently, Computer Science (randomized algorithms, `cooperative' phenomena in large communication networks), it has led to deep, fundamental mathematical research. Much of the rapid and successful development in this area is due to a remarkable combination of probabilistic, combinatorial and (complex) analytic techniques.