Of course, you can do the following thing in vue.js to determine if someone hit enter on your input:

<input @keyup="handleKeyUp" />

You most likely know the concept of modifiers in vue.js as well, right? To always call event.preventDefault() on an event handler, you can do

<input @keyup.prevent="handleKeyUp" />

Did you also know, that for common command keys there are also modifiers that call the handler only for given key?

<!-- this will be only called when enter key is released -->
<input @keyup.enter="handleEnterKey" />

See the list of modifiers here. Since v2.5.0 it got even better and you can react on all key names defined in KeyboardEvent.key if you kebap-case them. Like:

<!-- this will be only called when enter key is released -->
<input @keyup.page-down="handlePageDownKey" />