How plants develop and acquire their form is a complex issue driven by a multitude of factors. Like all biological phenomena, the processes underpinning plant development are complex both when viewed collectively, but often also when simplified and viewed in isolation from one another. Computational tools can therefore be helpful means to deal with, and make sense of, biological issues. In this thesis, four different projects are considered that each deal with distinct biological questions connected to the development of aerial plant tissues, and particularly how they acquire and maintain their shapes. A particular focus is put on using an integrative approach that combines experimental data, computational tools, and mathematical models to help forward our understanding of morphodynamic processes in the plant shoot. Firstly, a method is presented for segmenting and quantifying geometric properties in plant shoots on the tissue level. The method is applied to analyse and identify phenotypes in a broad range of different mutants, over many plants. Specifically, this high-throughput approach identifies transport proteins of the fundamental plant hormone auxin, ABCB1 and 19, as potential regulators of shoot and flower morphology. The method is also shown to be useful in identifying and parameterising plant shoots. Finally, the method is applied on a range of mutants with compromised genes involved in cell wall synthesis, where it is found that the spatial gene expressions for these have implications for shoot morphology. Secondly, a quantitative approach is used to analyse the spatial patterning of auxin signalling in initiating leaves, which is believed to have importance in the development of leaf morphology. Nuclear segmentation of ratiometric auxin reporters in 3D provide insights into how auxin is not symmetrically patterned in the early stages of leaf development, in contrast to previous belief. Thirdly, extending on the issue of auxin patterning, a quantitative approach is developed to identify the patterning of the auxin efflux transporter PIN1 in plant shoots, specifically in the context of flower organ initiation. A method is developed to investigate molecular patterning data of PIN1 from many samples, in 3D. The results indicate that PIN1 patterning is tightly linked to the initialisation of new flower organs, supporting the notion of PIN1 as a primary driver of phyllotactic patterning. However, in contrast to a recent study, the analysis shows strong convergence patterns of PIN1 polarity at initiation sites. This data is then complemented with a mathematical model simulating auxin transport driven by the extracted PIN1 data. Strikingly, it is found that whilst auxin patterning in the shoot follows that of PIN1, the two are not always similar, and local auxin maxima can appear in the tissue even before clear PIN1 concentration maxima or convergence patterns do so. Lastly, a high-throughput analysis of plants with compromised functionality of POM2/CSI1, a linker protein between cellulose synthase complexes and microtubules, is conducted. Methods from the above projects are integrated to assess phenotypes in mutant plants relative to wild-type both at cell and tissue scales. It is found that plants with defective POM2/CSI1 functionality have flattened shoot apices and compromised cell geometries. By analysing how cell geometry data is spatially patterned, and how these properties develop over time, a change in mechanical properties is assessed to be the primary cause of the phenotypes. A computational model is then used to demonstrate how reduced mechanical stiffness is sufficient to explain the flattened shoots. Collectively, the results in this thesis emphasise the applicability of computational methods in addressing questions in plant development. The integration of experiments, data quantification tools, and mathematical modelling of molecular patterning and mechanical regulation, illustrate a holistic approach to the research of these issues. As a result, this enables the investigation of questions where more singular approaches become limited.