A question that had bothered physicists for a long time,  Key to understanding Nuclear structure and the structure of matter in the universe, was "how heavy can atomic nuclei be?".  The first step in answering this came with the discovery that different arrangements of nucleons in a nucleus, like the electron orbitals in an atom, gave rise to different energies, called binding energies.  By knowing the positions of all the protons and neutrons in a nucleus, the exact binding energy could be calculated.  These calculations suggested that as with electrons, there was also a  shell structure associated with nucleons.  Certain structures, so-called "magic numbers", lead to particularly stable nuclei.  Significant examples of this phenomenon include the double magic nuclei helium 4, oxygen 16, calcium 40 and calcium 48, as well as lead 208. In these nuclei, both the protons and neutrons form filled shells, so that these nuclei all have particularly high binding energies.  

It was then discovered that nuclear shell effects could stabilize certain nuclei much heavier than Uranium, stable enough that theoretically, trace amounts could exist in nature and  a magic configuration, similar to lead 208, was anticipated for the isotope 298114 (114 protons and 184 neutrons).  Early calculations from 1966 predicted an "island of stability" in this region, with the isotope 298114 at its center. This was the birth of the idea of the superheavy elements (SHE), and marked the start of experimental efforts to synthesize them. 

To bring two protons close enough together and form a bond requires considerable energy.  To overcome the binding energy,  nuclei are accelerated through long tubes and collided in particle accelerators like the one at Berkeley, California.

Particle accelerator, UNILAC, Germany

It was thought initially that SHE would have halve lives similar to that of Uranium so once created in an accelerator they would remain long enough to be easily detected.  Unfortunately this wasn't the case and the first experiments suggested that either the calculations were wrong and the island of stability didn't exist, or nuclei being created were decaying instantly.

Modifications to UNILAC enhanced its detection capabilities and managed to overcome this problem and SHE were detected albeit in very low volumes.  The first success came in 1980 with the discovery of element 104, produced through the fusion of lead 208 and titanium 50.