Modern biological research is accumulating an ever-increasing amount of information on genes and their functions. It is apparent that biological functions can very rarely be attributed to a single genes, but rather arise from complex interaction within networks that comprise many genes. A fundamentally important challenge in contemporary biology is to extract mechanistic understanding about the complex behavior of genetic networks from the available data. The interactions within a genetic network are often exceedingly complex and no-linear in nature, and thus are not open to intuitive understanding. This situation has given rise to a host of mathematical and computational approaches aimed at in-depth analysis of genetic network topologies and dynamics. In particular these approaches focus on system level proprieties of these networks, not directly derivable from their constituent components. To a large extent the power of these theoretical approaches rely on meaningful reduction in complexity by utilizing justified simplifications and abstractions. The underlying principle is that in order to comprehend a mechanism, it is not necessary to take into account all the available information about the mechanism. Given this, Computational models that follow this approach focus on incorporating core components that are essential in answering a specific biological question, while simplifying/omitting the less relevant processes. A fundamental question is this regard is what simplifying concept should be employed when developing a theoretical model of a genetic network. A successful approach to address this question is the notion of network motif analysis. This approach is based on the core idea that most genetic networks are not arbitrary nor unique, instead they can be categorized into common network dynamics and topologies that perform core functions. Analogous to components of an electric circuit (resistors, capacitor, etc.) these network motifs have distinct properties that are independent of the network that they are embedded in. Therefore analysis of genetic networks in terms of their constituent motifs can potentially be an effective mean in obtaining mechanistic understanding about them. In this thesis the network motif approach is utilized to study two instances of pattern formation in plant tissues. The first study focuses on organization of stem cells within the shoot apical meristem of the model plant, Arabidopsis thaliana. The results demonstrate that three interconnected network motifs can account for a range of experimental observations regarding this system. Furthermore through an exhaustive exploration of the available data, candidate genes and interactions corresponding to these motifs are outlined, thus paving the way for future interdisciplinary investigations. The second study explores the development of vasculature during arabidopsis embryogenesis. In contrast to shoot apical mersitem in mature plant, the cell number and arrangement of vasculature in highly dynamic during its embryonic development. To account for this feature, a computational framework was utilized that is capable of capturing the interplay between genes and cell growth and division. The outcome revealed that two interlocking networks motifs dynamically control both patterning and growth of the vascular tissue. The study revealed novel spatial features of a motif previously studies exclusively in non-spatial settings. Furthermore the study resulted in a compelling example of model-driven discovery, where theoretical analysis predicted a specific cellular arrangement to be crucial for the correct development of vasculature. Subsequent analysis of experimental data confirmed the existence of this cellular arrangement in the embryo. The projects presented in this thesis exemplify successful applications of the network motif approach in studying spatial genetic network. In both cases the networks were successfully examined in terms of their constituent motifs, which subsequently lead to increased mechanistic understanding of them. Ultimately the work presented in this thesis demonstrates the effectiveness of studying genetic networks by a combination of careful examination of available biological data and a reductionist modeling approach guided by the concept of network motifs.