Model-independent measurements of the cosmic expansion history can shed light on the dark sector and current cosmological tensions. I will discuss past, present, and future efforts to constrain H(z) using two emerging and complementary probes: cosmic chronometers (CC) and gravitational wave standard sirens (GW). In the first part, I will present the CC method and recent results from differential age dating of intermediate-redshift passive galaxies. In the second part, I will discuss the standard siren method and forecasts for upcoming LIGO-Virgo-KAGRA observing runs and galaxy surveys. These two probes already provide an independent reconstruction of H(z), with direct H0 measurements from GWs and H(z) constraints up to z ~ 2 from CCs, and represent promising avenues to unveil the expansion history of the Universe.