We understand the strength of gravity far less well than most fundamental physical constants, to a level of accuracy comparable to about one centimeter on a 100 meter field. It is also not particularly well tested at very short ranges (micro-meter scales) and in very weak fields. A number of theoretical physics theories are looking for new physics in these domains.
New experimental tests limit how extreme the deviation from the Newtonian norm can be at the micrometer scale, and in the process rule out several possible theories of quantum gravity. New experiments are likely to produce even more accurate measurements over the next few years.
Also, always interesting are the latest musings of Jacob D. Bekenstein on alternatives to dark matter through adjustments to the equations of general relativity that could explain phenomena attributed to dark matter. He gets some constructive criticism in another recent paper that proposed a tweak to address a flaw the authors state that they have identified in his theory.
Another interesting paper about the phenomena sometimes called dark energy from a Greek scholar considering empirical evidence measuring the Casimir force concludes that: "with or without the presence of a compact extra dimension, vacuum energy with any suitable cutoff can not play the role of the cosmological constant."