As I write this, they're starting to pressurize the docking vestibule, and they'll be opening the hatches.
The amazing thing about all this is that the docking maneuver was completed entirely automatically; the spacecraft itself completed the docking maneuver from a 20-meter hold distance.
This is what the future looks like:
That's a simulation, the HUD display from the spacecraft's control system overlaid on a high-def image from one of the forward cameras on the thing, but that's what it would look like if you were flying the thing.
So now it'll be two hours before they actually open the hatches. I'm not staying up to see it; I'll watch the replay after I do get up.
But: privately-owned, reusable, man-rated spacecraft just docked with ISS. SpaceX is spoiling us with all this cool shit!