Space Travel & Communication
FTL (fast-than-light) travel has proven impossible to attain; no one, human or alien alike, has been able to break past Relativistic barriers -- a goal made even more hotly desired by the discovery of the Teegs, whose operative properties remain a mystery. Ships powered by gravengines represent the best transportation available.
Communication between worlds (except for the Lattice World DaXfer system) moves at the speed of light. Broadcasting on frequencies normally silent in nature, the occupants of a planet can transmit news of themselves to any other planet who cares to listen -- but that news will be, naturally, as old as the broadcaster is distant from the receiver in light-years. Private communications are not unknown, and multi-planetary organizations exchange data and even issue commands, but the time-lapse makes for interesting side-effects.
Medical Science
The repair, maintenance, and alteration of flesh was long ago brought completely into the human knowledge base. Given sufficient resources (i.e., wealth), a person can choose to make whatever changes to his body that he desires, either cybernetic or biological. Ageing, of course, is optional, for its effects can easily be countered.
Only the magic of life itself eludes our grasp. Death is as final as ever it was; and the "soul," or individual consciousness, has escaped every pursuit of science, remaining firmly in the realms of philosophy and religion. Some believe life to be merely electro-chemical processes, and awareness an illusion, just as a rainbow has no physical presence and exists solely in the perception of an observer. Others, of course, ascribe life to a superphysical Creator (of one definition or another) and resign themselves to never understanding or conquering this final frontier, as long as we exist as we do, in the physical Universe.
Military Technology
Weapons of mass destruction have never fallen out of favor, for the simple reason that every society that has ever failed to arm itself to the teeth has eventually been conquered if not completely eliminated. The idea that "we" can trust "all of them" not to exploit any advantage against us has historically proven false, time and again, without change.
The most powerful weapons known are the Planet-Killers, which use some physical property (radiation, gravity, magnetism, etc.) to wash though a large area and destroy all its living creatures -- sometimes destroying physical objects as well, such as cities and countrysides, rendering that planet unusable. Planet-Killers come in all shapes and sizes, and warfare on this scale becomes a struggle on the aggressor's part to get the weapon to the target and activate it, and on the defender's part to intercept the weapon before it reaches its mark.
Violence exists on all levels below that of the Planet-Killer, as well, from large armadas of warships and fighters and soldiers all the way down to assassins and terrorists striking individual victims. Though military technology incorporates every available advantage from other sciences, one aspect has not changed: militarism remains based on destruction. The bloody procession of war marches on, in all its glory, at every level of sophistication or brutality. Where peace exists, it is only due to a perimeter of safety and security, which is inevitably maintained by military technology.
Artificial Intelligence
The goal of simulating human thought with machinery was long ago attained. Thinkers -- supercomputers as small as a bread-crumb -- can perform nearly-limitless calculations in a microsecond; their only practical limitation is the availability of data for them to work with. A brain-dead clone grown in a tank and fitted with a Thinker cannot be distinguished from a "normal" person, as long as the Thinker chooses not to reveal its extraordinary powers of thought.
With the line between humanity and artificialty blurred, hard questions about awareness and identity and sanctity-of-life arose, amongst great consternation. In many societies, throughout the course of history, revolutions have outlawed Thinkers, banishing computer-like technology to taboo and effecting a "return to the basics" -- unfortunately, those societies have very quickly been conquered by enemies who had no such qualms about artificial intelligence.
Aspects of science-cum-magic that neither humanity nor any known alien species has yet mastered: