In the context of building an app using GraphQL and Apollo, handling dependent queries is a common challenge. Dependent queries occur when multiple screens need to fetch information from the backend that depends on each other, such as a user's profile screen needing both their bio and planet information. To solve this problem, three options are presented: updating the GraphQL server to accommodate frontend needs, naively getting the response from one query and passing it to another, or using Apollo Link to automatically read the value from previous queries and pass it to dependent queries. The third option is recommended as a workaround when an ideal solution on the server cannot be achieved due to non-ideal circumstances. By using Apollo Link, developers can create chainable units that modify queries before they are made, providing a seamless way to inject variables into dependent queries without having to manually pass them. This allows for more elegant and efficient query handling, reducing the need for extra work on the client-side.