Every day automated algorithms make decisions that can amplify the power of businesses and governments. Yet as algorithms come to regulate more aspects of our lives, the contours of their power can remain difficult to grasp. This paper studies the notion of algorithmic accountability reporting as a mechanism for elucidating and articulating the power structures, biases, and influences that computational artifacts exercise in society. A framework for algorithmic power based on autonomous decision-making is proffered and motivates specific questions about algorithmic influence. Five cases of algorithmic accountability reporting involving the use of reverse engineering methods in journalism are then studied and analyzed to provide insight into the method and its application in a journalism context. The applicability of transparency policies for algorithms is discussed alongside challenges to implementing algorithmic accountability as a broadly viable investigative method.