For the first time: iCloud.com portal accessible from iPhone and Android through browser
The iPhone is able to log in directly while remaining in the browser (without redirection) to access photos, notes, reminders and the Find My iPhone option. However, the page still suggests that for other functionality you will have to use a desktop computer or an iPad.
The situation is similar when logging in from a device running Android. The interesting part is that, however, if you have enabled two-factor authentication, you will still need your iPhone around to access the account. Having said that, if you have been using your Android device for two-factor authentication, you will still be able to use it as usual.
Even though Apple has been taking their time to provide this functionality, users can now profit from it without the need of a desktop computer, even on Android. The important thing to remember is that you need your iPhone around if you have additionally protected your iCloud account with two-factor authentication and that not all features are available without a desktop computer or an iPad.