Starting with 1.4.0 release Vue Storefront is supporting Magento2 product reviews. Unfortunately, Magento2 REST API doesn't contain any Reviews-related endpoints, so to make it work you need to install an additional Magento2 module.
Installation steps (in your Magento2 directory):
config repositories.divante vcs https://github.com/DivanteLtd/magento2-review-api.git composer require divante/magento2-review-api:dev-master php bin/magento setup:upgrade
You should be aware that Reviews are stored in the Elastic Search. To display Reviews correctly you need to update your mage2vuestorefront and run the Reviews sync:
node --harmony cli.js reviews