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Over the last half-a-century or so, the observations of the cosmic microwave background (CMB) have provided us with clues to the physics operating in the early universe. During the past decade, the detection of gravitational waves (GWs) from merging compact binaries by the Laser Interferometer Gravitational-Wave Observatory has opened up a new window to observe our universe. In this talk, I will initially describe the physics of inflation that is supposed to be responsible for the generation of the primordial perturbations and the constraints on inflation from the CMB. Thereafter, I will describe the manner in which the dynamics during the later stages of inflation and the phase of reheating (which connects the epochs of inflation and radiation domination) can lead to the generation of primordial GWs of strengths detectable by the ongoing and forthcoming GW observatories. I will conclude the talk with a discussion on the recent observations by the pulsar timing arrays that point to a stochastic background of GWs and the possible implications of the observations for the physics of the primordial universe.