A highly structured tissue is formed from an unstructured accumulation of cells during morphogenesis. The pioneering works by Thompson, Turing and Meinhardt introduced physical principles allowing the breaking of symmetry, i.e. the emergence of patterns. This started an ongoing effort to understand the physics behind morphogenesis. In this thesis I will analyze spatial and temporal aspects of morphogenesis for different biological systems in separate parts. The planarian is an ideal model animal to understand mechanisms of spatial body axis formation. This is due to the possibility to measure its body orientation field which utilizes the orientation of the cilia of the planarian’s ventral tissue. Moreover, their astonishing regeneration capabilities allow extensive perturbation experiments. I propose a minimal model which demonstrates the emergence of the wild type body orientation as well as the development of dual-head body orientation due to beta-Catenin RNAi treatment. The topological defects of the body orientation field are calculated on a lattice for simulations and lattice-free for experimental data. These topological defects are a robust way to analyze and compare experiments with simulations. My minimal model reveals sufficient components and mechanisms for robust body axis regeneration. The second important aspect of morphogenesis is the growth regulation of tissues which is often driven by cell proliferation. The regulation of growth is not only important during growth, but also to maintain homeostasis. As fast renewing tissues are very dynamic they may have more pathways of morphogenesis active than non-renewing tissues which points to mechanisms of morphogenesis. The in vivo measurement of this proliferation rate is a challenging task. In this thesis the analysis of DNA labelling assays and the carbon 14 dating method are extended. The carbon 14 dating method can be used to determine cell renewal rates on time scales as long as the lifetime of organism last. Moreover, this method can be applied for tissues in any terrestrial organism because it utilizes the change of carbon 14 in the atmosphere due to atmospheric nuclear bomb tests in the 1960s. The method is extended to gain a better understanding of the tissue dynamics of liver, muscles and amygdala. On the other hand, the DNA labelling assays are used to estimate cell cycle parameters for fast cycling cells. The measurements are fatal to the samples and involve plenty of labor resulting in few sampled data for a time series. The deterministic Nowakowski model is extended to a stochastic model accounting for cell-to-cell and sample-to-sample variability to fully exploit the information contained even in the fluctuations of the data points. A comprehensive parameter recovery study with synthetic ground truth data is performed to evaluate the models. The new stochastic model shows no bias, a good accuracy and scales well with the number of measurements in contrast to the deterministic text-book method. I conclude with proposed applications of my new models and methods that can advance our understanding of growth and pattern formation during morphogenesis. All python software developed in this thesis is shared as open source and a website makes the stochastic analysis of DNA labelling assays available to experimentalists in a user-friendly way.