I'll agree with Yaa101 that a big part of the story is the picking of low-hanging fruit, or to put it less metaphorically, that in the first 100 years of institutionalized science (let's say 1850-1950 without getting caught up in the exact dates), there were a lot of fundamental questions that could be addressed through the application of relatively systematic, rigorous observation and experimentation, and modeling with the kind of math you can do on a chalkboard.

Within this time period, though, a lot of these questions were addressed and the new questions that arose required more data, better instrumentation, and more advanced mathematical modeling techniques to address.

In my own field (geology, in particular tectonics and earthquake studies), this was laid out in a very explicit manner: the fundamental mode of observation is geologic mapping, and the terrestrial surface of the earth slowly got mapped. The mapping of the past may be refined or re-interpreted but rarely does it need to be redone from scratch. It is done to a reasonable level of resolution. There is still a lot of unknown under the ocean basins, but we have strong theoretical and empirical arguments for why those areas are not as complex as continents and therefore less interesting.

The late 1960s through the mid 1980s saw the development of plate tectonic theory which completely revolutionized the science. Now, 50 years in, we have some second- or third-order questions but most of the first-order questions have been addressed.

Today, the major developments of the field come from better instrumentation, for the most part. In the sub-field of tectonics, progress comes from the development and application of new methods for dating rocks or other geologic features (including things like exposure dating or 'how long as this rock been at the surface of the earth'), and from using satellite-based measurements of earth deformation (GPS and radar interferometry) to actually measure the motion of tectonic plates and sub-plates. Additional, continuous refinements in seismic imaging of the subsurface (driven by the oil industry primarily) has also been very helpful.

This stuff is really expensive! It's hard to go camp out, hike a bit, make some observations, and write a good paper. The instrumentation to get the age of rocks might cost $100,000 and then when consumables and salary are factored in it might cost $500-$2000 per sample. You might need 10-20 samples to really find out anything new in your 10-km by 10-km area of interest. And I believe that geology is quite cheap relative to high-energy physics or whatever. Major geophysical experiments can cost millions. We piggyback on physics and other tech to a large extent---launching GPS satellites for example, or using obsolete particle accelerators for geochemical measurements. The oil industry spends (tens of?) billions a year acquiring data as well but very little of it becomes public or available to researchers, though the cumulative data release from industry is significant. [NB, I may be 1 order of magnitude short on any of these numbers.]

In general there have been very few major theoretical advancements in the past 20-30 years. We have gotten better at recognizing coupling between tectonic process and earth surface processes, and as instrumental datasets slowly increase (as we observe more earthquakes, etc.) some smaller boxes get checked. However, a geologist from the mid-1980s would be able to navigate today's scientific landscape pretty well. The fads are different but like any fashion, many are cyclical and were fads in the 80s too.

I personally see advancement coming from better statistical and numerical modeling, and the availability of high-quality global datasets (primarily created through large international collaborations, which is a post-cold war thing). I also see a lot of room for improvement in our understanding of the coupling of mechanisms spanning vastly different timescales--for example earthquakes occur in seconds, post-earthquake phenomena last weeks to decades, the earthquake cycle lasts hundreds to thousands of years, and the cumulative deformation from earthquakes and related processes is what we call 'tectonics' over millions of year timescales. It's really hard to make a single numerical (i.e., finite element) model that works over all of these timescales and is driven by basic physics (i.e. an earthquake results from forces applied rather than being imposed). Nonetheless there are almost certainly a lot of really important coupling processes that occur on these different timescales but they are really hard to analyze (and a lot of interesting stuff happens at 20 km depth and at mm/yr rates, which is pretty damn hard to observe).

So I guess I see a lot of 21st century science as bridge building rather than outright discovery. This is fine. An analogy would be moving to a new country. The first bit is the discovery of the place, then you learn what language they speak. The learning doesn't stop there. As you learn the language, a lot of daily stuff makes sense. As you gain an understanding of the culture and the history, and can interact in a meaningful way, the value of that learning continues to increase, but it doesn't feel like 'discovery' like it did in the first year.