As suggested in official docs you could use mitt library to dispatch events between components, let suppose that we have a sidebar and header which contains a button that close/open the sidebar and we need that button to toggle some property inside the sidebar component :

in main.js import that library and create an instance of that emitter and define as a global property:

Installation :

npm install --save mitt

Usage :

import { createApp } from 'vue'
import App from './App.vue'
import mitt from 'mitt';
const emitter = mitt();
const app = createApp(App);
app.config.globalProperties.emitter = emitter;
app.mount('#app');

in header emit the toggle-sidebar event with some payload :

<template>
  <header>
    <button @click="toggleSidebar"/>toggle</button>
  </header>
</template>
<script >
export default { 
  data() {
    return {
      sidebarOpen: true
    };
  },
  methods: {
    toggleSidebar() {
      this.sidebarOpen = !this.sidebarOpen;
      this.emitter.emit("toggle-sidebar", this.sidebarOpen);
    }
  }
};
</script>

In sidebar receive the event with the payload:

<template>
  <aside class="sidebar" :class="{'sidebar--toggled': !isOpen}">
  ....
  </aside>
</template>
<script>
export default {
  name: "sidebar",
  data() {
    return {
      isOpen: true
    };
  },
  mounted() { 
    this.emitter.on("toggle-sidebar", isOpen => {
      this.isOpen = isOpen;
    });
  }
};
</script>

For those using composition api they could use emitter as follows :

Create a file src/composables/useEmitter.js

import { getCurrentInstance } from 'vue'

export default function useEmitter() {
    const internalInstance = getCurrentInstance(); 
    const emitter = internalInstance.appContext.config.globalProperties.emitter;

    return emitter;
}

And from there on you can use useEmitter just like you would with useRouter:

import useEmitter from '@/composables/useEmitter'

export default {
  setup() {
    const emitter = useEmitter()
    ...
  }
  ...
}

On version 3 of Vue.js, you can use either a third-party library, or use the functionality written in the publisher-subscriber(PubSub concept) programming pattern.

event.js

//events - a super-basic Javascript (publish subscribe) pattern

class Event{
    constructor(){
        this.events = {};
    }

    on(eventName, fn) {
        this.events[eventName] = this.events[eventName] || [];
        this.events[eventName].push(fn);
    }

    off(eventName, fn) {
        if (this.events[eventName]) {
            for (var i = 0; i < this.events[eventName].length; i++) {
                if (this.events[eventName][i] === fn) {
                    this.events[eventName].splice(i, 1);
                    break;
                }
            };
        }
    }

    trigger(eventName, data) {
        if (this.events[eventName]) {
            this.events[eventName].forEach(function(fn) {
                fn(data);
            });
        }
    }
}

export default new Event();

index.js

import Vue from 'vue';
import $bus from '.../event.js';

const app = Vue.createApp({})
app.config.globalProperties.$bus = $bus;

Content of EventBus class file:

class EventBusEvent extends Event {
  public data: any

  constructor({type, data} : {type: string, data: any}) {
    super(type)
    this.data = data
  }
}

class EventBus extends EventTarget {
  private static _instance: EventBus

  public static getInstance() : EventBus {
    if (!this._instance) this._instance = new EventBus()
    return this._instance
  }

  public emit(type : string, data?: any) : void {
    this.dispatchEvent(new EventBusEvent({type, data}))
  }
}

export default EventBus.getInstance()

usage in project, emit event:

import EventBus from '...path to eventbus file with class'
//...bla bla bla... code...
EventBus.emit('event type', {..some data..}')

listen event:

import EventBus from '...path to eventbus file with class' 
//...bla bla bla... code...
EventBus.addEventListener('event type', (event) => { console.log(event.data) })