The impact of respiratory virus infections on the health of children and adults can be very significant. Yet, in contrast to most other childhood infections as well as other viral and bacterial diseases, prophylactic vaccines or effective antiviral treatments against viral respiratory infections are either still not available, or provide only limited protection. Given the widespread prevalence, a general lack of natural sterilizing immunity, and/or high morbidity and lethality rates of diseases caused by influenza, respiratory syncytial virus, coronaviruses, and rhinoviruses, this difficult situation is a genuine societal challenge. A thorough understanding of the virus-host interactions during these respiratory infections will most probably be pivotal to ultimately meet these challenges. This review attempts to provide a comparative overview of the knowledge about an important part of the interaction between respiratory viruses and their host: the arms race between host innate immunity and viral innate immune evasion. Many, if not all, viruses, including the respiratory viruses listed above, suppress innate immune responses to gain a window of opportunity for efficient virus replication and setting-up of the infection. The consequences for the host's immune response are that it is often incomplete, delayed or diminished, or displays overly strong induction (after the delay) that may cause tissue damage. The affected innate immune response also impacts subsequent adaptive responses, and therefore viral innate immune evasion often undermines fully protective immunity. In this review, innate immune responses relevant for respiratory viruses with an RNA genome will briefly be summarized, and viral innate immune evasion based on shielding viral RNA species away from cellular innate immune sensors will be discussed from different angles. Subsequently, viral enzymatic activities that suppress innate immune responses will be discussed, including activities causing host shut-off and manipulation of stress granule formation. Furthermore, viral protease-mediated immune evasion and viral manipulation of the ubiquitin system will be addressed. Finally, perspectives for use of the reviewed knowledge for the development of novel antiviral strategies will be sketched.