There's a standard for this using NFC and UWB, Digital Car Key; BMW has support for either 2.0 (NFC) or 3.0 (UWB) across their entire range. The Hyundai Motor Company group (Hyundai/Kia/Genesis) is starting to add support as well. See [1] for exact models (look for the little key icon). Several other makes are members of the Car Connectivity Consortium that standardized this protocol so it's reasonable to expect wider compatibility in the near future. The protocol incorporates significant countermeasures against relay and replay attacks like some that are mentioned in other comments here.

[1]https://www.apple.com/ios/carplay/available-models/

On my Ford I just walk up to it and it's unlocked and I can start it without taking my phone out of my pocket. I pretty much never carry an actual key on me.

Tesla also has the key card, which you could just put in your wallet.