The COVID-19 pandemic has generated a huge volume of research from various disciplines, such as health sciences, social sciences, mathematical modeling, social network analysis, complex systems, decision-making processes, computer simulation, economics, among many others. One of the key problems has been to understand the diffusion processes of the virus, which quickly spread worldwide through transport networks, mainly air flights. Almost two years after start the pandemic, it is necessary to collect and synthesize the existing work on this matter. This work focuses on studies related to the COVID-19 contagion simulation through transport networks. In particular, we are specially interested in the different datasets and epidemiological models used. The search methodology consists of four exhaustive searches in Google Scholar carried out between January 2020 and January 2021. Of the 1786 findings, we chose 53 articles related to Covid-19 contagion modeling and simulation through transport networks. The results show 30 different data sources for the collection of air flights and 11 additional sources for maritime and land transport. These datasets are usually complemented with other data sources, local and international, with demographic information, economic data, and statistics of traceability of the pandemic. The findings also found 15 spread models of contagion, with the SEIR model being the most widely used, followed by mathematical-based risk models. This diversity of results validates the need for these types of compilation efforts since researchers do not have a single centralized repository to collect air flight data.