Molecular communication (MC) is gaining increasing popularity for data communication between nano systems. First applications both in the biomedical and the industrial domain show that MC is often better suited than conventional radio communication. Theoretical studies regarding the communication capabilities are accounting for information-theoretic metrics to maximize the system performance concerning the communication rate, the bit error rate, and the delay. However, the freshness of status updates by means of MC is still a topic to be addressed in this field. The concept of the age of information (AoI) has been introduced to particularly analyze and design timely system updates when considering the limited capabilities of the underlying communication channel. In this paper, we introduce the AoI concept in molecular communication channels. In particular, we focus on the peak age of information (PAoI), which describes the maximum AoI on a per packet basis. We derive a theoretical equation to compute the average PAoI metric. This allows analyzing the trade-off between an increased rate of transmission (thereby a reduced latency) and the produced inter-symbol interference (ISI) (thereby an increased error rate). We further validate our analytical results by means of simulation and illustrate the impact of the channel parameters. We finally summarize open research problems to conclude the discussion of AoI in the field of MC.