We compare different methods for long-term  earthquake forecasting or for time-dependent forecasting. Long-term forecasts are obtained by smoothing historical seismicity. A first method for time-dependent forecasts is based on a statistical model of seismicity ("ETAS"), which assumes that every earthquake can trigger other earthquakes with a rate that decays in time according to Omori's law. We have also developed a new method for earthquake forecasting, which
is purely statistical and  makes no assumption about earthquake physics. In this model, past earthquakes are smoothed in space and time using adaptative Gaussian kernels. While being much simpler than ETAS, the performances for earthquake forecasting are almost as good. Finally, we have developed another model for earthquake forecasting that couples adaptive smoothing of past seismicity to estimate present seismicity rate with a physical model of earthquake triggering ("rate- and-state", Dieterich 1994) to extrapolate seismicity rate in the future. This model provides the best results for longer time scales of the order of weeks or months.