Recently, organic bioelectronics has attracted considerable interest in the scientific community. The impressive growth that it has undergone in the last 10 years has allowed the rise of the completely new field of cellular organic bioelectronics, which has now the chance to compete with consolidated approaches based on devices such as micro-electrode arrays and ISFET-based transducers both in in vitro and in vivo experimental practice. This review focuses on cellular interfaces based on organic active devices and has the intent of highlighting the recent advances and the most innovative approaches to the ongoing and everlasting challenge of interfacing living matter to the "external world" in order to unveil the hidden mechanisms governing its behavior. Device-wise, three different organic structures will be considered in this work, namely the organic electrochemical transistor (OECT), the solution-gated organic transistor (SGOFET - which is presented here in two possible different versions according to the employed active material, namely: the electrolyte-gated organic transistor - EGOFET, and the solution gated graphene transistor - gSGFET), and the organic charge modulated field effect transistor (OCMFET). Application-wise, this work will mainly focus on cellular-based biosensors employed in in vitro and in vivo cellular interfaces, with the aim of offering the reader a comprehensive retrospective of the recent past, an overview of the latest innovations, and a glance at the future prospects of this challenging, yet exciting and still mostly unexplored scientific field.