Vue.js: Simple click function not firing

The best way to do this is to use the .native event modifier.

For example:

<my-custom-component @click.native="login()">
  Login
</my-custom-component>

Source: https://v2.vuejs.org/v2/guide/components.html#Binding-Native-Events-to-Components

When you do :

<page-change page="bio" @click="changeThePage"></page-change>

That means that your are waiting page-change component emit the click event.

Best solution (thanks to @aeharding) : Use .native event modifier

<page-change page="bio" @click.native="changeThePage"></page-change>

Solution 1 : emit click event from child component :

Vue.component("page-change", {
    template: "<button @click='clicked' class='btn btn-success'>Button</button>",
    props: ["page"],
    methods: {
       clicked: function(event) {
         this.$emit('click', this.page, event); 
       }
    }
})

For information event is the default value passed by Vue for native event like click : DOM event

Solution 2 : emit directly from parent component :

Vue.component("page-change", {
    template: "<button class='btn btn-success'>Button {{ page }}</button>",
    props: ["page"]
})

var clients = new Vue({
    el: '#show_vue',
    data: {
        currentRoute: window.location.href,
        pages: [
          'bio', 'health',
          'finance', 'images'
        ]
    },
    methods: {
        changeThePage: function(page, index) {
            console.log("this is working. Page:", page, '. Index:', index)
        }
    }
});

<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.2.5/vue.js"></script>
<div id="show_vue">

  <span v-for="(page, index) in pages" :key="index+page"
        @click="changeThePage(page, index)">
  
    <page-change :page="page"></page-change>
    
  </span>

</div>