DOM element to corresponding vue.js component

The proper way to do with would be to use the v-el directive to give it a reference. Then you can do this.$$[reference].

Update for vue 2

In Vue 2 refs are used for both elements and components: http://vuejs.org/guide/migration.html#v-el-and-v-ref-replaced

Just by this (in your method in "methods"):

element = this.$el;

:)