If you are wondering what Inbox is, read the announcement. I'll only be talking about what I have noticed about it since I started using it.
The fundamental ideas behind Inbox are great. Yes, I receive too much email. Yes, some of it I do not need to read and never will need to. Yes, some of it I will need to deal with, but I cannot right now. And yes, some of it is quick enough or important enough that I should deal with it right now. Inbox is the best way that I have seen of dealing with all of those cases in one place.
Inbox was clearly designed with mobile in mind first. The one-column organization and vertical navigation are suited very well to a phone. Swiping a message left or right to snooze it or mark it as done feels very natural, especially if you are on Android (think about the notification tray). The fact that you can snooze/mark as done from a notification is the icing on the cake. I do wish that I could swipe sideways while a message is open, either to snooze/mark as done or to navigate from one conversation to another like in the Gmail app.
The desktop version needs some work. It has the exact same layout as the mobile version, one column. We solved this issue a long time ago in Gmail: let the list of messages take up one column, and open messages alongside it in another column. Images are displayed awfully; I received a screenshot taken on a phone, and it was almost twice the height of my screen. Swiping obviously is not an option, so there are buttons on each message for snoozing/marking as done. It doesn't feel as cool as swiping the message away, but it is still a lot better than having to select a message and then looking around at the top to find the archive button. It is also only available on Chrome. They say that other browsers are coming soon, but what better way to test it than to let people who got into the invitation only program try it on whatever they prefer? Not to mention that this is an unacceptable abuse of Chrome's position as the most popular browser. Isn't the point of web applications that they are platform agnostic? I have also noticed that the amount of memory Inbox takes up slowly increases over time. This was not scientifically tested, just something I noticed.
Bundling messages together in a visual stack instead of tabs feels much better, in particular on mobile. It also makes it very easy to perform an action on all messages in that bundle. I am confused as to why a bundle's name will show up when there is only one message present in that bundle. I don't want to have to open the bundle to get to a message if there are no other messages in the bundle. Allowing the user to create their own bundles makes them infinitely more useful than the predefined tabs in Gmail. Any filters you already created in Gmail will be preserved in Inbox and can be made into a bundle easily.
Speaking of preserving things from Gmail, all actions that you make in Inbox happen in Gmail as well. Marking something as done in Inbox archives it in Gmail, and probably vice versa. However, not everything from Gmail has made its way over to Inbox. For example, in Gmail old chat logs can be found, but they will not show up in Inbox. It also does not allow you to edit contacts.Gmail will obviously have to coexist with Inbox until they make their way over or are fleshed out into their own product. I am not sure it would be a good idea to bring them into Inbox, as its strength comes from its simplicity and cleanliness. Priority markers did not make the journey either, but they were clearly on their way out when tabs were introduced to Gmail.
I approve of reminders being brought into Inbox. It makes sense, because the act of snoozing a message essentially makes it into a reminder. It would not make sense to have one sort of reminder in Inbox and another in Google Now. The presence of reminders is another motivator to keep a clean inbox; if you have a bunch of messages cluttering it up, the reminders will not stand out to you. Gmail clearly intended for its users to archive messages when they were done with them, but it never encouraged that behavior the way Inbox does. And for that, I am sold. Plus, look at what happens when you have nothing in your inbox: