Abstract: Gravitational waves (GWs) provide a unique probe of the early universe, as they can travel almost freely from their generation to the present. I will discuss two cosmological GW sources: primordial GWs from quantum fluctuations during inflation and scalar-induced GWs (SIGWs) produced by curvature perturbations at horizon reentry. Both can reveal the universe’s thermal history. In particular, I will highlight how a non-standard reheating phase imprints distinctive features on the GW spectrum, and how the Big Bang nucleosynthesis (BBN) bound constrains the high-frequency tail of primordial GWs. I will also discuss the recent pulsar timing array (PTA) results and their possible interpretation as SIGWs, which may shed light on early-universe dynamics. Finally, I will briefly address the gauge issue of SIGWs and describe how to define a gauge-invariant observable by constructing a generalized idealized detector including second-order effects.