Seven months after replacing traditional passwords with single-use SMS codes, Yahoo is taking the next step toward blowing up the password altogether. The company today announced Yahoo Account Key, which links your account to a mobile device and then asks you to approve new logins through push notifications. It's part of a broad redesign of Yahoo Mail designed to make the service faster and easier to search, and also lets you use the app with accounts from Outlook, Hotmail, and AOL for the first time. (No Gmail, though, at least not yet.)

Here's how Account Key works. You link your Yahoo account to a mobile device, most likely a smartphone. When you go to log in to Yahoo Mail on the web, enter your email address and tab down to the password. Yahoo will recognize that the account has the feature enabled and send a push notification to your device. You can approve or deny the login directly from the notification.

Account Key resolves a number of common problems with passwords: that you forget them; that you reuse them for multiple services, making you more vulnerable when one of those services inevitably is hacked; that you don't have a second method of authentication in case someone else ever gets their hands on your password. In a demonstration for reporters on Wednesday, Account Key looked like a quick and elegant way to move beyond passwords. Yahoo says the feature will eventually roll out to other company services.

Meanwhile, if you're a Yahoo Mail user — and hundreds of millions of people are. Hi, Aunt Kathy! — there's lots to like about the new apps for Android and iOS, which were developed under the code name "Mail Plus Plus." The new app connects to your social networks to bring in current pictures of your contacts, which appear alongside your messages. It also pulls in real-time contact details from those networks, so you can tap on any of your friends and see their phone number and other details, if they've shared them.

The app has added Mailbox-like swipe gestures (for deleting messages and, more less usefully, "mark as unread"), and you can highlight multiple messages by long-pressing on any of them. It also upgraded its search box — type in a couple letters of a contact's name, and Yahoo Mail organizes the results into messages, photos, and non-picture file attachments. (That's a nice touch: most people using Yahoo Mail for personal reasons are probably looking for photos; most people using it for work will probably appreciate having their spreadsheets and presentations in a standalone view.) All of this works across accounts — even if you've added your Hotmail and AOL accounts to your Yahoo account (stop laughing), Yahoo Mail will pull search results from all three into a single place.

If you're someone who regularly sends emails to yourself because you're using your inbox as a to-do list, Yahoo is taking extra-special care of you. You can long-press the compose button to create an email with your name in the To: field, and the cursor already placed in the subject line. "Email yourself" is also now a 3D Touch icon in the iOS version of the app. (I understand many people use their inboxes as to-do lists; inboxes basically require you to think of them as to-do lists — but emailing yourself strikes me as a suboptimal way of getting almost anything done. That's a rant for another day, though!)

The new apps look good, appear to work much faster than than their predecessors, and have meaningfully advanced the fight against passwords with Account Key. I only wish Yahoo had waited to launch until they supported Gmail — the standard email service for the younger generation that Yahoo has been courting so aggressively with its mobile apps. (Look at the goodwill, not to mention daily users, generated by Microsoft's Gmail-supporting Outlook app.) But if you're using an email service founded in the 1990s, the new Yahoo Mail takes several steps in the right direction, and I suspect current users will like it a lot. Whether it will attract many new ones, though, is far less certain.