Even though solar physics is a well-established field, the number of unsolved fundamental questions is surprisingly large. What is the strength and direction of magnetic fields on different scales and at different heights? Why is the corona hot? When will the next solar flare occur? To probe these open questions, we rely on a combination of challenging observations, complex modeling, and analyzing a wealth of data. In this talk, we will discuss some of the recent advances in observations, modeling, and data analysis. Using GREGOR as an example, we will explore how our observing capabilities can be improved, discuss approaches to measuring turbulent quiet Sun fields via high-precision spectropolarimetry, and how techniques from computer science can help us cope with vast amounts of data that can no longer be analyzed manually.