SpaceX will attempt to launch five Falcon 9 rockets [nasaspaceflight.com] in April. This includes an International Space Station (ISS) resupply mission and a mission to launch Bangabandhu-1, Bangladesh's first satellite. The Bangabandhu-1 launch is planned [nasaspaceflight.com] to be the first to use SpaceX's Falcon 9 Block 5 [wikipedia.org] rocket, which may be the final major iteration of Falcon 9 before replacement by BFR [wikipedia.org].
At a South by Southwest (SXSW) panel, Elon Musk said that SpaceX could test the Big Falcon Rocket (BFR) "spaceship" as soon as the first half of 2019 [spaceflightinsider.com]. The spaceship is the second stage of the complete BFR rocket, would be capable of reaching orbit without the first stage booster, and alone has over 50% more thrust than an entire Falcon 9.
The initial tests would likely be similar to the Grasshopper [wikipedia.org] vertical takeoff and landing tests.