The problem of automated personality classification (APC) is defined as a task of assigning personality characteristics (traits) to a person, based on information about that person, and the content that person produced. In this paper, we investigate important aspects of this problem and give an overview of the existing solutions that solve it. As a scientific contribution, we present a hierarchical classification of the existing solutions to this problem. We also propose several new research directions regarding the problem of APC. Firstly, we investigate possible improvements of the existing solutions to the problem of APC, for which we use different combinations of the APC corpora, psychological trait measurements, and learning algorithms. Afterwards, we consider extensions of the APC problem and the related tasks, such as dynamical APC and detecting personality inconsistency in a text. This entire research was performed in the context of social networks and datamining algorithms.