How to deal with cross-account access in AWS IAM

When I was preparing for my AWS Developer exam, something that I could barely wrap my head over was IAM. AWS IAM, Identity & Access Management, is the core of the whole AWS architecture and it is presented in the either first or second chapter in every AWS tutorial. At the first glance, it looks easy. But after passing my exam and having done some hands-on management work for the whole organization of the company, I realized it is maybe the most complicated product AWS provides.