<p>This paper uses Poisson autoregressions to forecast earthquakes and heatwaves in Italy. Statistical modelling of counts of earthquakes and high temperatures is of fundamental importance for estimating risks involving natural disasters and climate changes. Four different Poisson models are put under scrutiny in terms of forecasting performance: a standard Poisson model with constant rate; a Poisson autoregressive model; a Poisson autoregressive model with covariates; and a self-excited threshold Poisson autoregression model. The standard mean square forecast error and the average forecasting score are used to evaluate the forecasts. A Monte Carlo study is first carried out. Then, two empirical applications on earthquake data for Italy and on temperature data for six Italian cities are offered. For the earthquakes, the best forecasting performance is achieved by the Poisson model with covariates. In case of temperatures, the results are more mixed for the forecasting score measure, while the Poisson autoregressive model with covariates prevails in all the cases when using the mean square forecast error.</p>