With the remarkable increase in the number of scientific entities such as publications, researchers, and scientific topics, and the associated information overload in science, academic recommender systems have become increasingly important for millions of researchers and science enthusiasts. However, it is often overlooked that these systems are subject to various biases. In this article, we first break down the biases of academic recommender systems and characterize them according to their impact and prevalence. In doing so, we distinguish between biases originally caused by humans and biases induced by the recommender system. Second, we provide an overview of methods that have been used to mitigate these biases in the scholarly domain. Based on this, third, we present a framework that can be used by researchers and developers to mitigate biases in scholarly recommender systems and to evaluate recommender systems fairly. Finally, we discuss open challenges and possible research directions related to scholarly biases.