Technology in the world of Retro is different from ours. First, due to the Divergence, it has developed in a radically different direction. It's a world in which integrated circuits were developed very late and even then their popularity was limited, as people preferred the more resistant and reliable vacuum tubes. Second, the technology has progressed beyond our current level, with development up until the 2050's.
One of the key elements of the backstory are the Resource Wars, fought for the last remaining energy resources on Earth. In the wake of the crisis, as the economy ground to a halt, the United States sought alternatives to fossil fuel energy, arriving at two solutions - utilizing fission and fusion as the primary power sources. The first crude fusion cell was unveiled in 2066, providing the United States with an edge and averting its imminent bankruptcy.
Fission power sources have found their use as well, as power sources for robots, which can utilize a nuclear power unit as its energy source or backup generators
In the 2050's, due to the oil crisis, gasoline was no longer a viable car fuel, even more so with the excellent power the automobiles had. As such, many car companies have desperately pursued research into alternative power sources, with Chryslus Motors finally patenting the successor to gasoline: electric engines, powered by energy cells. Charged with fusion cells, a Chryslus Corvega or Highwayman featured 800+ horsepower and acceleration from 0 to 60 MPH in under a second, all done with a full analog system and no computers. However, not many of these cars were produced and those that were had a limited success due to their hefty price tag ($199,999.99 for a Corvega).
A fledgling field of science in our world has become a thriving industry of its own in the world.Retro Robots are widely used and have reached a very high level of refinement and advancement. They can operate individually, can process visual and audio data in real time and make tactical decisions in the heat of the moment, operate human or inbuilt weapons with deadly accuracy and even host artificial intelligences.
An indication of just how advanced robotics were is the fact, that robots were commercially available to civilians and companies, apart from the military - Mister Handy and protectron robots being the best examples of just how widespread and popular they were.
One of the most noticeable technological leaps was made in the field of protecting people from harm (as well as causing it, but more on that later). The United States was especially proficient at doing so, as its research into polymers paid off, resulting in suits of advanced combat armor being widely deployed across the country to police and military forces, sometimes even civilians with a special BADTFL permit. This armor protected the wearer considerably from conventional and explosive damage as well as laser and plasma, a trait quite useful on the modern battlefield.
Another example of considerable advancement is the power armor, an armoured suit with a hydraulic endoskeleton, powered by a fusion pack, designed to be a one-man tank replacing traditional, inefficient vehicles in their role. It is an exclusively American technology, which is also the root of many other technologies, such as the aforementioned cold fusion.
An interesting example of research into personal protection exists, in the form of the Tesla armor, a suit based on Nikola Tesla's blueprints, in which Tesla Attraction Coils attract and disperse energy attacks, providing a surprisingly effective protective apparel and another example of how Retro Worlds physics are different than our own.
Likely the single field in which the greatest advancements were made, weaponry of the Retro world is varied and incredibly advanced in some regards. Apart from conventional weapons based on combustion of gunpowder, energy weapons development advanced at a rapid pace, allowing for the creation of mass produced laser, plasma and pulse rifles.
Yet another startlingly advanced field in the Retro world, biomedical science flourished in the retro-futuristic world. The most basic example, the stimpak is astounding by our standards - a self contained stimulation delivery package, sending the cells into a replication frenzy, swiftly healing minor wounds, doing in seconds what often takes days by regular means. What further deepens the gap between our technology and that of Fallout is the existence of superior versions, the super stimpak and Ultra stimpak, which can heal even the worst of injuries at a minor cost of health damage from the frenzy of replication a few minutes later.
Of course, developments also took place in fields other than healing, namely, pharmaceutical enhancement. In comparison, our drugs look like primitive hallucinogenics, as those in the Fallout world last longer and have much stronger effects. Buffout, synthetic steroids, amplifies Strength and Endurance greatly, Mentats increase Intelligence and Perception while psycho increases both resistance to pain and physical damage.
Yet all of the above pales in comparison with truly revolutionary technologies. Beginning with the ability to easily clone replacement limbs and organs for humans, through surgeries permanently enhancing the human body all the way to viruses capable of rewriting human DNA and altering their physical appearance in real time. This last, most phenomenal achievement is called the FEV, Forced Evolutionary Virus.
Compared to other fields, computers are strangely primitive - while portable units (such as RobCo Pip-Boys) and robots exist, it seems that the actual processing power is quite low (64k of RAM in Terminals), contrasting with other advanced technologies. Their frames are also typically large and blocky, compared to the small, sleek forms of today. One of the main reasons for this is that the computers in the Fallout universe are based on a mismatch of integrated circuits and vacuum tubes. Reason for this is uncertain, although it is possible that there simply was a monopoly on advanced computer manufacturing - many robots would seem to require much more computing power than is available for common computers around the wastelands, and there were some supercomputers in existence - most of them owned by the U.S. government.
Another example are displays, all CRT with no LCDs.