We're still stuck using Chemistry.
Hyrdogen and Oxygen burn fast. Controlled-explosion gets you off the ground. Gliding, friction and parachutes get you back.
A little improvement in technology gets you a little better rocket ship. But you're still stuck using the Chemistry of Hydrogen and Oxygen (and the various solid fuel-based ways of storing the two elements to get a controlled explosion later.)
Nuclear doesn't sound like the next wave except for deep space exploration satellites. Plasma engines give you a good boost in deep space over a long period of time but it doesn't get you off the ground or the moon or Mars.
Until we get a new form of Energy (not based on Chemistry or dangerous Nuclear), we're stuck doing what we're doing now. Slightly better crafts as slight technology improvements come on stream.
New physics, anti-gravity, something else is needed to make the next step.
Actually, just a new material able to withstand the stresses of being used for an orbital elevator.