Falcon Heavy launches this summer. They're targeting July 1st for the wet dress rehearsal (fueled up, practice countdown) and launch soon after.
The test stand at their McGregor Texas facility is nearing completion, and the 3 cores (center core and 2 liquid fueled boosters, all based on Falcon 9R) are under construction at Hawthorne, California. The pad mods at KSC LC-39A are progressing rapidly.
Falcon Heavy will be the most powerful rocket on Earth, capable of sending 53,000 kg to low Earth orbit, 21,200 kg to geostationary orbit, or 13,200 kg to Mars.
53,000 kg is more than the weight of a fully loaded Boeing 737-200.
Falcon Heavy concept of operations (CONOPS) video below, showing how the cores will return and land at KSC-13 after launch.
The plan for the booster cores to return to LC-13 immediately after separation, about 4-5 minutes after launch. The center core is to return a few minutes later when launching lower mass payloads. For heavier payloads it'll continue downrange, land on an Autonomous Spaceport Drone Ship (ASDS), partially refuel, then relaunch and fly back to LC-13.
There is currently one ASDS stationed at Jacksonville, Florida. Another is under construction for their Vandenberg AFB launch site in California, and a third is likely for their Mars Crossing spaceport near Brownsville, Texas.
The new launch platform under construction at KSC LC-39. Looks like they're going to build a ramp to it over the old Saturn V/Shuttle gravelway.
The new horizontal integration facility (HIF) will be built just outside that pad perimeter gate. Its foundation is curing and should be occupied in a few weeks..
Did some screen caps from the video,