There are a few different ways to answer that question. In the way I suspect you intended it, the answer would be that there was a flurry of development up through the 1800s that, for the most part, define the modern instrument. Two critical ones: the iron frame allowed for expanded range and power, and the double-escapement action facilitated rapid note-repitition. More recently, a critical--and generally negative--change came when ivory keytops were replaced with plastic ones. The problems that creates are still being worked out.

And there are still innovations being made, but it is difficult, if not impossible, for them to gain a foothold. My own piano, for example, was rebuilt by a local technician, Ed McMorrow, who has developed a technique for modifying a standard piano action such that, in my experience, the touch and tone of the instrument are unequalled. Another local innovator has pattened a mechanism that gives an upright piano action the feel of a grand. (To which I will attest. I've never encountered a comparable upright.) He is reasonably well-known amongst pianists in the area, but neither his nor Ed McMorrow's innovations are likely to become generally adopted. I have heard about experiments elsewhere with creating a quarter-tone piano. I'm afraid I don't remember the name of the experimenter.

It also could be argued that the most important modern changes to the piano is its re-invention as an electronic instrument. One can argue about whether it is still a piano, but certainly electronics eliminate many of the acoustical instrument's limitations. It's interesting to consider the possibility that in the same way that today it is widely accepted that Bach will be played on a modern piano, eventually it may be equally accepted to hear Beethoven performed on electronic ones.

Yes - I thought of the electronic piano.  However, I would argue that the touch element of an acoustic instrument cannot be electronically replicated, at least not yet.