Understanding the magnetic properties of materials arising from their atomic structure still poses many questions especially if effects like quasiperiodicity and disorder are taken into account. The project SpinsInQuasicrystals aims to obtain a better understanding of the magnetic properties of the material class of quasicrystals. A special focus is given to disorder phenomena in these systems, which are an intrinsic property of quasicrystals and have been hardly addressed in the research of quasiperiodic spin systems yet.The interest in the properties of quasiperiodic systems has grown significantly since the discovery of quasicrystals by Shechtman et al. in 1982 (Nobel Prize in Chemistry 2011). Quasicrystals are materials with a perfect long-range atomic order without having a three-dimensional translational periodicity but instead rotational symmetries which are forbidden for conventional crystals. Further, these materials can be classified to possess a degree of order intermediate between periodic and amorphous systems. Many physical properties of quasiperiodic systems are still not completely understood and also several new phenomena have been observed for these materials.During the project we systematically study the alignment of magnetic moments in quasiperiodic structures and disorder phenomena in these systems with numerical methods like Monte Carlo simulations as well as analytical techniques as e.g. spin-wave approximation and renormalization group approaches. The quasiperiodic materials are modeled as quasiperiodic tilings, which are suitable to describe the nonperiodic atomic structure of this material class and are commonly used for numerical and theoretical studies of quasicrystals.