A growing interest appears among public authorities and society in accurate and nearly real time aftershock forecasting to manage and mitigate post-seismic risk. Existing methods for aftershock forecasting are strongly affected by the incompleteness of the instrumental datasets available soon after the main shock occurrence. The deficit of observed events, in the first part of aftershock sequences, can be naturally attributed to various mechanisms such as the inefficiency of the seismic network

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... and the overlap of earthquake signals in seismic records. In this review, we show that short-term aftershock incompleteness can be explained only in terms of the second mechanism, whereas it is only weakly affected by the quality of the instrumental coverage. We then illustrate how standard models for earthquake forecasting can be modified to take into account this incompleteness. In particular, we focus on forecasting methods based on the data available in real time, in which many events are missing and the uncertainty in hypocenter location is considerable. We present retrospective tests that demonstrate the usefulness of these novel methods compared with traditional ones, which implement average values of parameters obtained from previous sequences.