The measurement of the local expansion rate of the Universe, the Hubble constant, has recently triggered an important scientific debate. It has been found that this quantity, when measured with local probes, shows a 4-sigma tension with the one extrapolated from the analysis of the high-redshift Universe with Cosmic Microwave Background. This issue, often referred to as the ‘Hubble tension’, is now one of the hot topics in physics. Exploring new and complementary approaches to measuring how the Universe (and the structures therein) have evolved has, therefore, become fundamentally important. This will increase the accuracy of the measurements and keep systematic effects under control. In this talk, I will discuss different approaches and methods that can be pursued to obtain independent constraints on the Universe’s expansion rate, recently reviewed in Moresco et al. (2022). I will present how cosmic chronometers, the ages of the oldest star in the Universe, and gravitational waves can be exploited as cosmological probes and how they can provide fundamental information in modern cosmology in the future.