Silicon Valley startup Udelv claims to have made the world's first public road test deliveries. (They brought groceries from Draeger's Market in San Mateo to two nearby customers.) The truck was in "test mode," whatever that means, and had a human driver able to take over from the automated driving if necessary.
Their trucks are electric, and house 18 secure cargo compartments with automatic doors. I guess the recipient goes outside and has access via the app to one of the compartments to grab their groceries. (They can also track the location of the truck using the app, like Uber.)