The concept of isotopes developed from radioactivity. The pioneering work on radioactivity by Henri Becquerel, Marie Curie and Pierre Curie was awarded the [https://www.nobelprize.org/nobel_prizes/physics/laureates/1903/ Nobel Prize in Physics in 1903]. Later Frederick Soddy would take radioactivity from physics to chemistry and shed light on the nature of isotopes, something with rendered him the [https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1921/ Nobel Prize in Chemistry in 1921] (awarded in 1922).
The question of stable, non-radioactive isotopes was more difficult and required the development by Francis Aston of a high-resolution mass spectrograph, which allowed the separation of different stable isotopes of one and the same element. Francis Aston was awarded the [https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1922/ 1922 Nobel Prize in Chemistry] for this achievement. With his enunciation of the whole-number rule, Aston solved a problem that had riddled chemistry for a hundred years.  The understanding was that different isotopes of a given element would be chemically identical.
It was discovered in the 1930s by Harold Urey in 1932 (awarded the Nobel Prize in Chemistry in 1934). It was early on found that the deuterium content had a profound effect on chemistry and biochemistry.
In the linear approximation, the effect of isotopic substitution is proportional to the mass ratio of the heavy and light isotope. Thus chemical and biological effects of heavier isotopes of the “biological” atoms C, N and O are expected to be much smaller since the mass ratios for the normal to heavier isotopes are much closer to unity than the factor two for hydrogen to deuterium. However, it has been reported in 1930s, and then again in 1970s and 1990s, as well as recently, that relatively small changes in the content of the heavy isotope of hydrogen, deuterium, has profound effects on biological systems. These strong nonlinear effects could not be fully rationalized based on the known concepts of the isotopic effects. These and other observations make it  possible that isotopes have a much more profound importance than could ever have been imagined by the pioneers.
In 2011 [http://chem1.mbb.ki.se/?page_id=10 Roman Zubarev] formulated the isotope resonance hypothesis. It originated in the following, unexpected observation. Define ΔM = M - M, where M is the monoisotopic mass (e.g. O = 15.994915 Da) and M is the nominal (integer) mass, i.e., the number of nucleons (e.g. O = 16). ΔM is a constant in the whole Universe. Define ΔM = M - M, where M is the average isotopic mass (e.g. O = 15.999 Da on Earth). Obviously ΔM depends on the precise isotopic composition for a given molecule. Finally define NMD = 1000ΔM/M and NIS = 1000ΔM/M, where NMD [in units of ‰] and NIS [in units of ‰] are the normalized isotopic defect and shift, respectively. If NIS is plotted as a function of NMD for a large number of terrestrial peptides, one would anticipate a homogenous distribution of data points (as in Fig. 1B). This is not what was found by Zubarev's team, instead they found band gap in the distribution with a narrow line in the middle (Fig. 1A).
This serendipitous discovery led Zubarev to formulate the isotope resonance hypothesis.