In the early spatial point process literature, point patterns were typically small, observed in 2D, had quite simple interaction structures, and there were no repetitions available. The observed point patterns were assumed to be realizations of stationary and isotropic point processes, and e.g. clustered patterns were typically modelled by assuming conditional independence between the cluster points given the Poisson distributed parents. However, large data sets (with repetitions) observed both in 2D and in 3D have become more and more common and it is less likely that stationarity and/or isotropy assumptions hold and that simple interaction structures are enough for realistic modelling of the data. In this talk, I will describe two examples of more complicated data sets where such a simple set-up is not enough. The first example concerns nerve fibre patterns on the epidermis, the outermost living layer of the skin. The spatial structure of nerves plays an important role in understanding how the nerve structure changes due to some small fibre neuropathy. The termination points of the nerve fibres form clusters around the base points of the nerves and even the parent (base) points tend to be clustered. In addition, the daughter points may not be located independently of each other, nor of the other parent points. The second example concerns air bubbles in polar ice. The air bubble patterns deep down in the ice are not isotropic (and some noise bubbles may occur in the data). Being able to estimate the deformation (anisotropy) can help physicists to determine the age of the ice at different depths.