I use Compose key for this, surprised nobody mentioned it here yet. This way it works in all X11 apps (Sway supports this out of the box as well), with no need for extra software or some specific desktop environment.

Just put something like

  <Multi_key> <semicolon> <parenright>  : ""
  <Multi_key> <t> <u>                   : ""
  <Multi_key> <t> <d>                   : ""

in your ~/.XCompose.

Yes, you have to put all the emojis you want there manually, but I use very few of them so it works for me.

EDIT: HN removed the emojis from my snippet. The double quotes there contained smiling face, thumb up, and thumb down.

My n00buntu derivative has some emojis and other logograms out of the box, eg. lines 326–337 of /usr/share/X11/locale/en_US.UTF-8/Compose:

  <Multi_key> <C> <C> <C> <P>             : ""   U262D # HAMMER AND SICKLE
  <Multi_key> <O> <A>                     : "Ⓐ"   U24B6 # CIRCLED LATIN CAPITAL LETTER A
  <Multi_key> <less> <3>                  : "♥"   U2665 # BLACK HEART SUIT
 
  <Multi_key> <colon> <parenright>        : ""   U263A # WHITE SMILING FACE
  <Multi_key> <colon> <parenleft>         : ""   U2639 # WHITE FROWNING FACE
  <Multi_key> <backslash> <o> <slash>     : ""      # PERSON RAISING BOTH HANDS IN CELEBRATION
 
  <Multi_key> <p> <o> <o>                 : ""  U1F4A9 # PILE OF POO
 
  <Multi_key> <F> <U>                     : ""  U1F595 # REVERSED HAND WITH MIDDLE FINGER EXTENDED
  <Multi_key> <L> <L> <A> <P>             : ""  U1F596 # RAISED HAND WITH PART BETWEEN MIDDLE AND RING FINGERS

Unbutchered: http://ix.io/2SsC

Oh, those are in Debian, as a matter of fact!

https://github.com/kragen/XCompose for those who prefer a more methodical approach.

There's also https://github.com/salty-horse/ibus-uniemoji if you want something a little more interactive.

I wrote https://github.com/sphaerophoria/ibus-memebox for myself because I wasn't quite happy with the performance of any of the solutions I found.

And another character picker for Rofi:

https://github.com/fdw/rofimoji/

GNOME has Ctrl+period.

KDE has one, too. Not sure what the default was, I remapped it to Super+Period

I use KDE and I've never tried it before. Win+. works!

Does it? I am in stock gnome and this shortcut isn't bound by default. What distro are you using?

I believe it has to be a GTK app - which almost none of the things I use on a daily basis are. Try in gedit or something like that.

My daily drivers are IntelliJ, Firefox, Chrome, and Terminator so it's not super useful to me... :'(

Check out this extension: https://extensions.gnome.org/extension/1162/emoji-selector/

It implements a system level emoji keyboard that you can trigger with <Super + e>. It works pretty great and on all apps, I use it a lot.

Oh wow, you are totally right, that does work in GTK apps. My daily drivers are about the same :(

It doesn't do anything for me. Can you point to a doc?