General Relativity
The general theory of relativity seems to be a bit (unnecessarily) overcomplicated in its current form, and a new, simpler approach might make it more conceivable and imaginable, moreover could render it prototypical for further analogous geometrical-based explanations and descriptions of the laws and regularities in the world (which is obviously not the case with its present version). The main problem with it is that Einstein had chosen to interpret the gravitational (and theoretically any other) force as a structure of the spacetime, and was compelled to use the very complicated Riemannian geometry to describe this structure, when gravitational (or other) forces appear in the spacetime (which remained Euclidian only for the cases without any forces, i.e. as an inertial one). The Riemannian geometry has the sole purpose (in this model) to assure that a straight worldline of the Minkowski spacetime gets bended under the effect of a gravitational mass, and that the former straight configuration becomes invalidated or "forbidden". The new bended line is the very same that it was before applying the gravitational force to it, but this force (or rather the body behind this force) caused the entire spacetime structure to warp, and so the worldline also had to bend with the spacetime, and now it has a new, curved appearance and configuration (which is completely congruent with the shape that would be necessary to describe the motion of that object in a gravitational field).
The problem with this approach is its (needless) complexity, which is caused by the fact that in this model all the forces and effects must be combined altogether into one single space(time) structure, and after this combination they cannot be handled and analyzed separately further. They are incorporated, literally amalgamated into each other, possibly resulting in a very (very) complicated structure, and without providing any ability to decompose it into its constructing elements. We simply lose a lot of information during the warping and force-applying process, and so we cannot reconstruct from the end result the initial configuration, since the Riemannian geometry only describes the current space structure, but not the effects, which caused this exact configuration to appear (thus forgetting this information forever). To illustrate the problem, let's suppose that we have a handful of plain, two-dimensional, single-colored geometrical shapes, and we put these over each other with some overlapping, one after the other. At some point we will have a very complex structure as a result, which to describe in itself would require a very advanced geometry, but which configuration could be easily reconstructed if we registered each new shape and its position during the overlaying process, i.e. if our model would contain this information as well, and at any time we could ask it about the individual shapes and their positions composing our current (possibly very complex) structure.
In the general relativity a gravitational mass and its field is used only so long as it warps the spacetime into a new structure, after which the model forgets completely about it, and any new masses introduced in the spacetime affect this structure itself again, thus making it more and more complex with each single step, without providing any ability to decompose it into its constituting parts. The opposite way would be much more advantageous, i.e. if we could dissolve the effect of a single gravitational mass already into simpler parts, which parts then would influence each other in a way that eventually would cause the worldline in the Minkowski space to bend. So, instead of warping the structure itself, it could be a better method to continue using a plain Euclidian 4-dimensional spacetime (or 3-dimensional for a 2-dimensional space etc.), and to assume myriad of very simple geometrical (invisible) figures throughout this space, which are grasping, grabbing or clasping each other and are trying to bend the other figures to their own shapes, thus causing in end effect a curved worldline (as they each attempt to pull it into their own position). This model obviously should not really take care of the resulting structure (it can be recomputed anytime), but it must register all these simple geometrical figures all over the space, and follow their interactions among themselves, until a balanced situation has finally developed (note, that this interaction process is not playing inside the spacetime, but in another (mental) dimension, and appears immediately (or in a very short time) in the physical spacetime with its result). With this approach the difficulty of the problem would remain a quantitative one (instead of evolving into a qualitative complication), since the spacetime structure stays the same during the whole process, and only the numbers of the simple geometrical shapes increases, as new masses are integrated into the system (just like in the example above each new added figure increased the number of the shapes but not the overall complexity of the problem). And at any time we could also remove any mass body from the system (with the result of removing its corresponding little shapes around it), and we could also separate the various subregions of the spacetime from each other, conducting our research only in one of them.
Of course, it could sound a bit fantastical that we have invisible geometrical shapes throughout the spacetime grasping and bending each other, but this should be imagined only as a helping method to decompose the gravitational effect (or any other regularities and rules) into smaller, more manageable parts, without associating any real existence with these figures. The advantage of this approach could be immense: we would get a much more conceivable and imaginable general theory as a result, which could also be used in many other situations. In fact, a brand new branch of the geometry could emerge from this idea, which would deal with the hypothetical interactions of small and simple geometrical figures, with the methods, how they can bend each other, how they try to hold their own shapes and how they affect the forms of the other shapes. (Of course, this whole process would play in a pure geometrical, non-physical dimension, so these figures would have no material, and their interactions would be based solely on their geometrical features and characteristics.) Furthermore, the laws and regularities of such a system would manifest themselves as the results of these interactions, since various geometrical configurations could be favored or banned according to the tendencies in the grasping and bending behavior of the small figures constituting this system. E.g., in the example above, the straight line would be forbidden after applying a gravitational force to it, because the geometrical shapes around the gravitational mass would pull this worldline into a bended position, and would not allow it to remain straight. Thus, we would not need to warp the spacetime structure itself to force this straight line to get curved, since, although the space structure itself would allow such a straight path, but with the current geometrical configuration the path is not maintainable anymore, as the geometrical shapes just pull it aside, effectively disabling this path in the space structure for this current configuration. Hence, any (ir)regularities could be defined as forbidden or invalid forms in the geometrical system, and the interactions between the shapes could be used to maintain these rules and to disable any possible digression by forcing the diverging object immediately into the right path through the grasping and bending procedure.
The first step in building this theory could be to construct a version of the general relativity, where the spacetime remains Euclidian during the whole time, and the worldlines are forced to bend by invisible simple geometrical shapes around the mass body. Of course, theoretically there are almost infinite number of solutions for this problem, and we should choose those, which solve the problem in the most elegant way (with the least numbers of figures, with the most simple shapes, with the most straightforward interactions, etc.). After that, we could generalize this theory to contain other physical regularities (electromagnetism, etc.), and then we could start to use this geometrical framework to describe complex rules and behaviors in other academic disciplines too, where the problems and situations can also be phrased in a geometrical way. For instance, we could build computers on a geometrical basis, where the computational rules are described in this geometric framework, and then play or simulate the interactions between the hypothetical shapes to impose the rules on the process and to come to an end result (e.g., in a very simple scenario, the multiplication rules could be represented as connection lines between two horizontal number lines, and geometrical shapes could be installed to bend all wrong lines into their right positions; then, by interpreting the vertical dimension as the time (or as procedure stages), we would finally have a computer capable of following the multiplication rules). Or, similarly, business rules and processes could be defined geometrically, and the framework consisting of the small shapes would automatically enforce these business rules and laws without any further interventions. Eventually, we would perhaps recognize that the regularities in our world could all be described best in a geometrical way, and the mathematical, physical, biological, psychological, sociological or any other rules are solely the different manifestations of the very same geometrically natured principles behind the various realms of the world.