Algolia is one of the most popular full-text search services. They have the libraries for different programming languages to integrate full-text search to the your application: For instance, you can implement the search page by Vue using the open-source library VueInstantSearch and at the same time implement a back-end using Laravel Scout to automatically add new entities to the Algolia. For the Vue front-end, they have a lot of predefined components such as Search Box, Autocomplete, Refinement List, Range Slider, Hits, Pagination, etc.
Laravel has its own package to support Algolia search engine, called Laravel Scout.
To install the Laravel Scout do: Under the hood, the Laravel Scout doing a lot of work but you just need to use the Searchable trait in your Eloquent model which you want to map to Algolia index (the index in Algolia is like a database).