Technologies can improve your performance in most areas of the game. They are passive bonuses that, once acquired, cannot be lost. Technologies can still be shared, sold, stolen or put up for auction, but this merely means that other players also gain this bonus, not that you are losing it.

Technologies sometimes show up as opportunities for investment, but are generally acquired by owning a research facility, which slowly develops new technologies, or by stealing them from another player. New technologies are always being developed, so this is only a partial list of available technologies:

Artificial intelligence administration: Increases income from financial institutions by 10%.
Automated turrets: Fortifications provide a passive +2 bonus to defend a location.
Commercial holograms: Increases income from entertainment providers by 10%.
Defensive matrix: Decreases casualties taken from battle by one unit.
Micro-filtering: Increases income from refineries by 10%.
Nano-manufacturing: Increases income from factories by 10%.
Neural resocialisation: Prevents your units of colonial militia from joining a rebellion.
Next-gen warp drives: Decreases cost of interplanetary travel by half.
Personnel cloaking: Ghosts gain an additional +1 bonus to all actions.
Space Construction Vehicles: Increases income from mining facilities by 10%.
Spider mines: Increases the combat value of vulture wings to 2 when defending.
Stimpacks: Increases the combat value of any army including at least one marine battalion by 1.
Yamato cannon: Increases the combat value of battlecruisers to 5 when bombarding.