The atmosphere, as any dynamical system highly sensitive to initial conditions, has a finite limit of predictability. This threshold affects our ability to anticipate the evolution of the climate system at all timescales, from the forecast of interannual anomalies some months ahead to the study of the sensitivity of climate statistics to slow-varying changes associated with global warming. This dissertation particularly focus on these two topics. On the one hand, a new precursory signal is introduced to improve the forecast and our understanding of El Niño-Southern Oscillation phenomenon, which represents the most prominent modulator of atmospheric variability worldwide and the major driver of climate teleconnections. On the other hand, the sensitivity of the distribution of European temperatures to the increasing concentration of atmospheric greenhouse gases is described, and used to infer projections of temperature-related mortality.The role of the oceanic RossBell dipole as a new premonitory signal for the onset of recent eastward-propagating El Niño events is established. This extratropical tracer is followed by El Niño events around 9 months later, but at the same time, it occurs a year after the development of a warm oceanic area in the western tropical Pacific region. This initial anomaly generates an anomalous atmospheric wavetrain extending eastward and poleward in the southern hemisphere, which is associated with the RossBell feature. Changes in the atmospheric circulation lead to warm ocean anomalies in the central tropical Pacific, being later enhanced by suppressed equatorial easterlies. These processes are linked to an eastward shift in the tropical convection, and thus a weakening of the Walker circulation, setting up the positive Bjerknes feedback that exponentially grows on top of the incipient warming and leads to the mature phase of El Niño.Changes in the distribution of European temperatures in a context of global warming are described from two different points of view. On the one hand, it is shown that the increasing intensity of the most damaging summer heat waves is mostly due to higher seasonal mean temperatures in summer, and not to specific changes in deseasonalized anomalies during extreme events. This result appears to be compatible with previous studies stating that future heat waves will be more intense, more frequent and longer lasting as a result of temperature rise. On the other hand, a simplified methodology is presented in order to reproduce the simulated changes in the temperature distribution from a relatively small set of parameters. Thus, the change in frequency, length and intensity of warm, neutral and cold temperatures is here derived from the evolution in only three central statistics of the temperature distribution, the mean, standard deviation and skewness.This simplified methodology is verified by testing the link between daily temperature and mortality data in nearly 200 European regions representing more than 400 million people. These relationships are later used to infer projections of mortality under greenhouse gas emission scenario simulations from an ensemble of state-of-the-art high-resolution climate models. Analyses point to a change in the seasonality of mortality, with maximum monthly incidence shifting from winter to summer. Results also show that the rise in heat-related mortality will indeed compensate the reduction of deaths from cold at the end of the century, unless a substantial degree of acclimatization to warm temperatures takes place, stressing the need for adaptation and mitigation strategies.