Slack supports both regular Unicode character entries for emoji, as well as short alpha codes which are converted into an emoji image when posted.
The setting to change emoji style can be found under the Preferences option inside the Team menu.
Unicode 9 Emoji Mockups
Slack Emoji Reactions
In addition to regular emoji use, reactions are also available.
Slack Emoticon Codes
The following codes convert emoticons into emoji images on Slack.