Quantum field theory serves as the universal language for understanding phenomena across particle physics, condensed matter physics, and gravity. Recent years have witnessed a paradigm shift in our understanding of global symmetries within quantum field theory and their various generalizations. At the same time, this is accompanied by a fruitful interaction between higher structures in algebra and geometry with field theory and models of gravity. This project aims to construct a robust bridge between these domains, with a focus on three interconnected research avenues. Firstly, we will explore tensor gauge theories, encompassing spins 1, 2, and higher, within the framework of generalized global symmetries. Such theories are relevant in the broad context of higher gauge theory and for the infrared structure of gravity, but they also provide effective descriptions of quasiparticles with restricted mobility, such as fractons. Secondly, we will extend the celebrated AKSZ construction of topological field theories to analyze non-topological models. These include gravity theories with and without torsion, foliated field theories, and Yang-Mills-like models, where we will develop novel localization techniques for precise computation of quantum observables. Lastly, using modern methods from the geometry of differential graded manifolds, we will construct an Einstein-like gravity theory on QP2 manifolds, exploring its physical implications in comparison to analogous studies in supergravity and double field theory. By consolidating the relationship between higher structures and field theory, this research endeavor will contribute significantly to the ongoing community effort to chart the space of quantum field theories, delineating those capable of furnishing effective descriptions for systems potentially realizable in Nature.