Spatio-temporal modelling of biological systems is a field of mathematical biology which has received a great deal of attention in recent years. This thesis is a contribution to this field with focus on modelling of biological growth patterns. Important examples are tumour growth and growth of plant populations. Two groups of spatio-temporal models are studied in the thesis, supracellular models and cellular models. The supracellular models describe how the boundary of a full-dimensional star-shaped object expands in time. The cellular models are based on spatio-temporal point processes and can describe other growth phenomena than the those described by the supracellular models. Finally, the thesis contains studies of shape analysis and non- stationary point processes, relating to stereological variance estimation and non-stationary spatial survival analysis.