Pas de résumé / This thesis consists in two separate parts: one on subcritical fracture experiments, and another one on earthquake statistics. The dynamics of these processes was mainly studied through their scale invariant dynamics, reflected in power law distri- butions of event sizes and times between events. The analyses focuses particularly on the variation of their exponent values and the origins of these variations. Subcritical fracture was studied by two experimental set-ups: creep experiments on paper, and constant-strain fracture of fibre bundles. Paper fracture has been studied in our group for more than 10 years now by visually observing the propaga- tion of the crack. We added acoustic emission monitoring to the experimental set-up in order to compare it to visualisation. The comparison between low frequency image analysis and the high frequency acoustic monitoring allowed to identify the impor- tance of the frequency of analysis for temporally correlated systems, and acoustic emission monitoring revealed the existence of aftershocks in the dynamics of paper fracture. The fibre bundle experiments concentrate on the temporal distribution of the frac- ture events, which follows an Omori law. We studied the influence of the temperature and stress on its exponent, and compared it with results from fibre bundle model analytical predictions and simulations. Our work on earthquakes was initially motivated by the results obtained on pa- per fracture experiments. Hence it starts by a study of aftershock sequences, their Gutenberg-Richter exponent, and the influence of the frequency of analysis on this exponent. By lowering the frequency of the time-magnitude signal we showed that at low frequencies the exponent of the Gutenberg-Richter law depends on the expo- nent of the Omori law. The last chapter of this thesis is concentrated on the early aftershocks. We in- spected the evolution of the properties of an aftershock sequence with time, and observed differences between aftershock occurring shortly after a mainshock, and late aftershocks. These results can be related to the recent proposition of existence of magnitude correlations in earthquakes