Elon Musk says Teslas should be able to navigate parking lots ‘by next year’
That'd be a big step up from the current Summon and Autopark systems.

Right now, Teslas can park themselves in both parallel and perpendicular spaces, but a person needs to be in the car and its capability is somewhat limited. CEO Elon Musk wants to build on that tech in a big way, and he believes it could happen pretty soon.
In a tweet responding to a clever use of Summon to avoid 2-hour parking regulations, Musk said "a slightly smarter version" of its Autopark and Summon technology could have cars driving around parking lots, finding spaces, confirming those spaces are valid parking spots and then parking -- all without human intervention, although the human likely has to be present in some regard.
For those unfamiliar, this uses Tesla Autopark/Summon. Slightly smarter version hopefully ready soon. By next year, a Tesla should be able to drive around a parking lot, find an empty spot, read signs to confirm it’s valid & park.
— Elon Musk (@elonmusk) October 31, 2018
Musk estimates that it could happen "by next year," but a year is a long time and it's unclear exactly when the automaker hopes to deploy that technology. There's always a chance it could be delayed for a variety of reasons, so don't hinge your hopes and dreams on a single tweet, but it's promising for people who either hate or are just plain bad at parking. It'd be a big leap forward.
Autopark as it currently exists requires the driver to identify a space by driving past it slowly until a P appears on the dashboard screen. The driver must then shift into reverse and hit a "Start" button on the touchscreen, at which point the car will maneuver itself into the space. Summon is a similar technology used to worm a Tesla into or out of tight spaces. This one can be used while outside the vehicle through the Tesla app -- engage Summon in the app, and the car will creep forward or backward slowly, based on user input. It can make slight steering corrections, too.
Musk has never been shy about his aspirations to have Teslas park themselves, and this is a technology he's brought up in the past. Hopefully, the actual deployment of this technology won't be too far off from Musk's own estimates. Last week, Tesla boosted the capability of its driver-assist systems with Navigate on Autopilot, which is an active guidance feature that claims it can help guide a car (with strict driver oversight, natch) from "on-ramp to off-ramp," including suggesting times to change lanes.