date works on strings if they contain well-formatted dates.
Input
{{ "March 14, 2016" | date: "%b %d, %y" }}
Output
Mar 14, 16
To get the current time, pass the special word "now" (or "today") to date.
Input
This page was last updated at {{ "now" | date: "%Y-%m-%d %H:%M" }}.
Output
Note that the value will be the current time of when the page was last generated from the template, not when the page is presented to a user if caching or static site generation is involved.