If it wasn't already obvious that Target is nervous about Amazon, it is now. Target has acquired another same-day delivery startup, Shipt, for a cool $550 million. The deal should speed up Target's plans to offer same-day delivery in its stores. It's expecting to have the feature available in half its stores by early 2018, and in the "majority" of stores in time for 2018 holiday shopping. Your options will largely be limited to groceries, electronics, "essentials" and home products, but Target plans to offer products from all its major categories by the end of 2019.
Shipt will continue to run its own business, which relies on a network of personal shoppers to fill orders, independently of Target. That creates an unusual situation where Target partners could compete against each other -- the big-box retailer also has an alliance with Instacart, creating a degree of overlap. This still gives you access to Shipt, however, and it'll be free to pursue partnerships that serve its core business. Ironically, it has a partnership with Whole Foods... you know, the store owned by Amazon.
The deal should close by the end of December. Provided it does, Target will join Walmart in scrambling to offer same-day delivery services as quickly as possible. They're clearly concerned that Amazon's widening same-day delivery plans and integration with Whole Foods will cut directly into their core businesses, and they're betting that you'll stick with them if you can get comparably hasty service.