All of iOS devices, Android 4.4+, and Windows 8.1+ can be displaying colorful emoji natively.
Unicode comes to version 14, and it has 1800 emoji across eight categories.
This page is an online web application; it tries to display all graphical emoji by using your system.
If your device doesn't support some of the emoji, the icon will be replaced with emoji's image. And those images can be copied as well.
This will automatically collect your most recent and frequently used icons.