Background/Objectives: The impact of the coronavirus disease 2019 (COVID-19) pandemic on health was significant worldwide. The measures adopted to limit the spread of the virus had an indirect effect on the epidemiology of other infectious diseases with similar mechanisms of inter-human transmission. The present literature review analyzed the scenario of pediatric acute respiratory infections in the post-lockdown period compared to the pre-pandemic and lockdown periods. The different patterns of viruses’ outbreaks were evaluated according to the type of local COVID-19 restrictive measures and to the type of pathogen. Methods: Relevant scientific literature published between March 2020 and November 2024 was identified by means of electronic keyword searches in the PubMed, Scopus, and Cochrane Library databases. Results: Worldwide implementation of non-pharmacological public health interventions aimed at limiting the COVID-19 pandemic resulted in a measurable effect on the circulation of other common respiratory viruses, significantly affecting their usual seasonality. Most viruses significantly reduced their activity during the lockdown period but returned to or exceeded historical levels after discontinuation of preventive non-pharmacological measures. For many respiratory viruses, particularly respiratory syncytial virus, an off-season increase was reported. Conclusions: The non-pharmacological interventions, which effectively helped limit the COVID-19 pandemic, resulted in relevant epidemiologic changes in most common respiratory viruses. Given the different seasonality and clinical severity observed for some pathogens after lockdown, possible future off-season or more severe epidemics should be expected.