Select, where JSON Array contains

JSON_CONTAINS() does exactly what you're looking for:

JSON_CONTAINS(target, candidate[, path])

Indicates by returning 1 or 0 whether a given candidate JSON document is contained within a target JSON document, or—if a path argument was supplied—whether the candidate is found at a specific path within the target. — 12.16.3 Functions That Search JSON Values

Currently, Laravel's query builder does not provide a corresponding API. There's an open internals proposal for it though.

In the meantime, you can execute a raw query:

\DB::table('users')->whereRaw(
    'JSON_CONTAINS(meta->"$.colors", \'["red"]\')'
)->get();

Which would return all users that have "red" in their meta->colors JSON field. Note that the -> operator requires MySQL 5.7.9+.

You can also call the whereRaw() directly on an Eloquent model.

Laravel 5.6

As of the 5.6 release, Laravel's query builder contains a new whereJsonContains method.

I think a way would be using the like operator:

User::where('meta->colors', 'like', '%"red"%')

However, this would only work if the values never contain the character " and the delimiters wouldn't change.