Why no underline?
John Gruber’s original Markdown mapped emphasis to <em> and <strong> only. On the web underline signals a link, so an underlined phrase that isn’t clickable confuses readers.
Use HTML
<ins>text</ins> means “inserted text” and browsers underline it. GitHub allows <ins>. <u>text</u> also works in most renderers that pass HTML through, and it is valid HTML5 for non-textual annotation.
Where HTML is stripped
Chat apps, some wikis and comment systems sanitise HTML. There you cannot underline; use bold or italic for emphasis instead.
Underscores are not underline
_text_ is italic in every Markdown flavour. Discord is the exception: __text__ underlines there, but that is Discord’s own formatting, not Markdown.