While they might not occur naturally on Earth, fusion reactions are constantly happening in our universe. Nuclear fusion reactions are responsible for the energy output of most stars, including our Sun.
When a star is initially formed, it consists of hydrogen and helium isotopes. Inside the star, these hydrogen isotopes collide in a series of multiple steps to eventually form helium nuclei.
The fusion reactions form a chain of sorts, helium to hydrogen then hydrogen to heavier elements. These reactions continue until the nuclei have fused into iron. The atomic mass of iron is close to sixty and at this point no more fusion occurs because it is energetically unfavorable due to the high binding energy inside an iron atom.
Once a star has converted a large fraction of its core mass to iron, it has almost reached the end of its life. At this point the fuel of the star is reduced so the fusion chain cannot continue. From here, most stars keep shrinking until they become a cooling ember made up of iron.
Credit: NASA, ESA, J. Hester and A.Loll (Arizona State University)
However, if a star is sufficiently massive a tremendous, violent, brilliant explosion can happen. A star will suddenly expand and produce more energy than our Sun will product in its lifetime. This explosion is called a supernova.
Many reactions occur during the supernova phase. Inside of the dying star, nuclei are accelerated to much higher velocities than in a fusing star. The added energy from their high speeds allow the nuclei to fuse and produce elements higher in mass than iron. The extra energy from the explosion is necessary to overcome the energy barrier to create a higher mass element. Elements such as lead, gold, and silver are all debris from past supernovae explosions.