In 1934, laboratory fusion was first performed by three scientists: Oliphant, Harteck, and Rutherford. Their paper was published in Nature Issue 133, entitled "Transmutation Effects observed with Heavy Hydrogen." The method they used is called beam-target fusion. A beam, a packet of particles moving in the same direction, to hit a piece of foil, also made of particles. Like billiards, where the first shot of the game, the white ball (beam) hits the racked balls (target), there results a lot of balls (particles) going in many directions. Unlike in billiards, some resulting particles were heavier, the products of the first fusion event on the surface of the Earth. Mankind then knew that fusion was possible in the laboratory.
Thus, began the massive task to figure out just how many variations of fusion were possible.
The contemporary concern at the time, was World War opponents and ex-allies, getting to the Golden Goose before 'our' side. The fear was an uneven advantage would be gained by the first to achieve greater fusion understanding. The question was, "Could fusion be weaponized?" A concern for any nation.
The second fusion type achieved by mankind in the lab setting was "beam-beam" fusion. The first selection of Periodic Table Elements to accelerate into each other, was followed by other Elements. Eventually, all the Elements in the Periodic Table have been fused, with every other Element, as was practical. All the Light Elements (Iron and lighter) have been cross fused with each other. The mathematical models were corrected to match the experimental data. Light Elements being fused with each Heavy Element (heavier than Iron), corrected the math model even further. Quantum Mechanics grew a sub specialty called Quantum Chromo Dynamics, or QCD, dealing with the mystery inside the atom's nucleus, where protons and neutrons rushed around other.
There remains a few untried combinations of Elements, due to the great difficulty in handling these last exotic Elements' nuclei. The approach was reversed, the math model came first, and is waiting for funding of a method that might have a good chance of fusing these very heavy, very exotic Elements.
Fusion now has many levels of fusion math modeling, from the simple (and incorrect) 'Ball' model, to a decent first approximation called Gamow Peak, using the Coulomb repulsion of positive Protons overcome, or rather tunneled through, via Quantum Mechanics, to a fifth level approximation, accurate enough for most all experiments. The complexity of fusion of Periodic Table Elements, including their isotopes, more than 2,000 isotopes, each fused with the other, creates a database of over 4 million possible, unique, fusion reactions. The atomic scientists decided to fund a central database, called EMPIRE, to not just hold this information, but to query it, with little effort.
The difficulty of 'knowing' fusion, being an expert, is not achieved by any single scientist today. Instead, it takes a group of fusion scientists, typically more than 5, each with their own sub specialty, to design a fusion reactor - that will work. ITER has taken over 3,000 scientists. The task is hard.
And yet, for the last 10 years, several teenagers have achieved fusion in their parent's garage. And over 80 adults have done the same. The "fusor" uses cheap, readily available deuterium, a heavy isotope of Hydrogen, in a spherical reactor around 4 inches in diameter, to create a self sustaining fusion ignition. Barely self sustaining, as there is no means to extract usable energy.
Mankind has come from doing fusion experiments in a 1 mile long accelerator, costing tens of millions of dollars, to family garage fusion reactors, for around $50,000.