The new severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) pandemic was first recognized at the end of 2019 and has caused one of the most serious global public health crises in the last years. In this paper, we review current literature on the effect of weather (temperature, humidity, precipitation, wind, etc.) and climate (temperature as an essential climate variable, solar radiation in the ultraviolet, sunshine duration) variables on SARS-CoV-2 and discuss their impact to the COVID-19 pandemic; the review also refers to respective effect of urban parameters and air pollution. Most studies suggest that a negative correlation exists between ambient temperature and humidity on the one hand and the number of COVID-19 cases on the other, while there have been studies which support the absence of any correlation or even a positive one. The urban environment and specifically the air ventilation rate, as well as air pollution, can probably affect, also, the transmission dynamics and the case fatality rate of COVID-19. Due to the inherent limitations in previously published studies, it remains unclear if the magnitude of the effect of temperature or humidity on COVID-19 is confounded by the public health measures implemented widely during the first pandemic wave. The effect of weather and climate variables, as suggested previously for other viruses, cannot be excluded, however, under the conditions of the first pandemic wave, it might be difficult to be uncovered. The increase in the number of cases observed during summertime in the Northern hemisphere, and especially in countries with high average ambient temperatures, demonstrates that weather and climate variables, in the absence of public health interventions, cannot mitigate the resurgence of COVID-19 outbreaks.