Spreading processes have been driving some of the most important changes in human society, such as pandemics that are caused by spreading of infectious diseases or technological revolutions led by innovation spreading. For this reason, modeling of spreading processes has gained a lot of scientific attention in the last decades that resulted in a wide range of approaches for their studying. In this talk, I will present models that offer a mathematical description of spreading processes and techniques that can help us understanding this dynamics. In particular, I will focus on challenges and differences between studying spreading processes in ancient times and modern times.