Epileptic seizures, epileptic spikes and high-frequency oscillations (HFOs) are recognized as three electrophysiological markers of epileptogenic neuronal systems. It can be reasonably hypothesized that distinct (hyper)excitability mechanisms underlie these electrophysiological signatures. The question is 'What are these mechanisms?'. Solving this difficult question would considerably help our understanding of epileptogenic processes and would also advance our interpretation of electrophysiological signals. In this paper, we show how computational models of brain epileptic activity can be used to address this issue. With a special emphasis on the hippocampal activity recorded in various experimental models (in vivo and in vitro) as well as in epileptic patients, we confront results and insights we can get from computational models lying at two different levels of description, namely macroscopic (neural mass) and microscopic (detailed network of neurons). At each level, we show how spikes, seizures and HFOs can (or cannot) be generated depending on the model features. The replication of observed signals, the prediction of possible mechanisms as well as their experimental validation are described and discussed; as are the advantages and limitations of the two modelling approaches.