Vue.js component for adding/removing items
It looks like the code makes good use of basic VueJS concepts and practices- using computed properties, binding values, conditional display with v-if, etc.

I also like the application of arrow functions, promise handling, etc.

I see there is a key attribute bound to the list items (i.e. v-bind:key="wrestler.id"). Correct me if I am wrong but that doesn't appear to be an attribute of &lt;li&gt;. What is that used for? Edit: Oh yes, thanks for reminding me about the key attribute for list editing

Then in the addWrestler() method, there are two .then() callbacks. Is there a reason not to move the three lines in the second callback into the first?

axios.get(this.action, { name: this.name })
    .then((response) =&gt; {
        this.wrestlers.push(response.data.data);
        this.busy = false;
        this.name = '';
        this.$refs.name.focus();
    })
    .catch(...)


If you really wanted to shorten the code for the promise callbacks, you could abstract those into methods.