There are a number of Japanese keyboard apps for Android devices, but the latest version of Android now comes with a default Japanese keyboard, iWnn IME. Enable it through "Language & Input" in the device's settings, making sure you check "Japanese" in the iWnn IME settings. You will be able to switch keyboards by holding down the spacebar on the English Android keyboard, and pressing the globe on iWnn IME. This default keyboard are much easier to use and switch between than third-party keyboard apps such as Simeji, which otherwise gets good reviews.
However, older versions of Android do not support Japanese input natively, and the Chinese handwriting keyboard (included with Android) will not produce Japan-only kanji. For these purposes, the handwriting keyboard 7notes With Mazec is a good solution (paid app), and the free app Simeji provides a third-party Japanese keyboard. Download these keyboards at the links below from the Google Play store and follow the instructions.
There are a wide variety of paid and free apps available in Google Play and the Apple App Store for use on mobile devices, to assist in doing research in Japanese as well as learning the Japanese language. This is an evolving list of some of the best and most useful apps for academic purposes.
Please see the information to the left and right for assistance enabling international keyboards on your phone and tablet, and instructions on accessing Japanese and American apps below.
Free apps cannot be downloaded from the Japanese Apple App Store (and podcasts subscribed to in iTunes) without a Japanese credit card. A Japanese credit card is required to even browse Japanese results within the App Store. You cannot access this part of the App Store through direct links from iTunes Preview. If you have a Japanese account and credit card, to access the Japanese App Store, click on the flag at the bottom right corner of the screen and choose Japan from the list of countries that comes up. This also works to change iTunes to Japanese iTunes on your computer or mobile device.
Japanese and American apps are not located different versions of Google Play; there is one Google Play site for all apps available for Android platforms. This means you can access all apps worldwide in Google Play via the Play store. Therefore, unlike the Apple App Store, you can download free and paid apps for Japan from the Google Play store directly. Searching in Japanese on Google Play tends to bring up English-language or United States-focused apps with keywords of the same meaning because your search terms and results are automatically translated. Thus, it is more difficult to find Japanese-language apps on Google Play, as opposed to the Apple App Store, which is language sensitive.
On iOS devices, installing international keyboards is done through "Settings." Go to General -> International -> Keyboards and choose the Japanese keyboard from the list. Keyboards can be switched by pressing the globe button at the lower left-hand corner of the keyboard screen (or on Logitech keyboards for iPad, shift+ctrl). Note that installing simplified or traditional Chinese handwritten keyboards allows for handwriting recognition within apps that support Japanese, but only kanji that are also used in China.