Epidemic models are increasingly applied in real-world networks to understand various kinds of diffusion phenomena (such as the spread of diseases, emotions, innovations, failures) or the transport of information (such as news, memes in social on-line networks and activity in functional human brain networks). We will mainly focus on Susceptible-Infected-Susceptible (SIS) epidemics on networks. We believe that the SIS Markovian epidemics on a given, fixed graph is one of the simplest "local rule - global emergence" models that allows a remarkable level of analysis. After a brief review of the SIS continuous-time Markovian process on a graph, we will show why SIS epidemics on networks are so interesting and we will overview our recent developments.