If you make judicious use of IoC containers (and Dependency Injection), you'll likely end up with lots of Bindings, some of which may look like:
I like to create my own library for any application. Similarly, I like keeping the "models" directory clean - I only add Laravel classes (Usually Eloquent instances) inside of the "model" folder.
Laravel encapsulates HTTP requests and responses within PHP objects. As you likely know, the HTTP core of Laravel revolves around Symfony's HTTPFoundation component.
Laravel uses Exceptions for error handling. This includes both HTTP error codes and application (run-time) errors.
Quick (and dirty) tip:
Frameworks provide a tool for rapid application development, but often accrue technical debt as rapidly as they allow you to create functionality.