Investigating the subsurface: this is one of the main tasks in the field of applied geophysics. And equally so in geology. But even if the aim is the same, the approach differs remarkably: on one side, methods based on physics, often combined with a substantial load of mathematical and numerical tools for processing and inversion; on the other side, the hermeneutic approach of geology, where a vast body of knowledge and sparse observations leads to, often qualitative, insights into the expected distribution of rock types and structures. Of course, these are the two caricatured extremes - in reality, there are many links between the fields, both in theory and also in practice. But arguably, the interaction is not always without tension. In this talk, we will explore a fruitful link, one that conceptualizes many commonalities in a qualitative and quantitative manner: geometry. Concepts from this field have been fundamental for centuries in both geophysics and geology. This ranges from the realization that many aspects of Earth's complex evolution can be simplified to 2-D manifolds within 3-D space, to the understanding that sharp discontinuities often produce discernible signals in geophysical investigations. This link has therefore been used implicitly for many years - but recent advances in computational geometry provide a more flexible integration of both aspects into modern inverse frameworks. In this talk, we will delve into the general concepts behind computational geometry, with a special focus on novel developments in the field. We will especially focus on low-dimensional parameterisations, which provide an efficient and flexible way to represent complex geological settings, but keep the possibility to integrate them into geophysical inverse frameworks. This link will be exemplified with joint geophysical-geological inversions using potential-field and electrical methods. A main advantage from this integration is the possibility to perform probabilistic inversion and uncertainty quantification, and to obtain meaningful posterior distributions for both, the geometric features, and the employed rock properties. Finally, we will venture into the realm of AI and investigate as to how the recent advances in foundation models will aid the understanding of geological context in the task of joint geological-geophysical investigations. One remarkable realisation has been that large pre-trained models may show emergent properties, which lead to a generalised representation of context for a wide range of applications, including geophysics and geosciences. After an investigation of current possibilities to use LLMs in inverse frameworks, we round off our journey by an educated look into the glass bowl about the evolving possibilities for a tighter integration of hermeneutic geological aspects and quantitative geophysical methods.