Hundreds of millions of people worldwide are affected by viral infections each year, and yet, several of them neither have vaccines nor effective treatment during and postinfection. This challenge has been highlighted by the COVID-19 pandemic, showing how viruses can quickly spread and impact society as a whole. Novel interdisciplinary techniques must emerge to provide forward-looking strategies to combat viral infections, as well as possible future pandemics. In the past decade, an interdisciplinary area involving bioengineering, nanotechnology and information and communication technology (ICT) has been developed, known as Molecular Communications. This new emerging area uses elements of classical communication systems to molecular signalling and communication found inside and outside biological systems, characterizing the signalling processes between cells and viruses. In this paper, we provide an extensive and detailed discussion on how molecular communications can be integrated into the viral infectious diseases research, and how possible treatment and vaccines can be developed considering molecules as information carriers. We provide a literature review on molecular communications models for viral infection (intra-body and extra-body), a deep analysis on their effects on immune response, how experimental can be used by the molecular communications community, as well as open issues and future directions.