Deciphering the principles of tumour growth dynamics is crucial for the development of new therapy concepts. Besides increasingly complex molecular investigations, mathematical modelling and computer simulation of selected aspects of tumour growth have become attractive within the last years. Here, we focus on the analysis of cancer invasion. Lattice-gas cellular automaton (LGCA) models allow for an adequate description of individual invasive cancer cell behaviour (microscopic level). We will show how analysis of the LGCA models allows for prediction of emerging macroscopic properties (in particular of the invasion speed). Furthermore, we will use our models for the interpretation of data from in vitro glioma cell invasion assays.