His research has focused primarily on the physiological, cellular, and molecular basis of circadian rhythms in mammals and more recently on the navigational mechanisms of migratory monarch butterflies.

His interest in science began in childhood with the cecropia moth—an insect made famous by Harvard biologist Carroll M. Williams, who used the moth in his pioneering work on the role of juvenile hormone in molting and metamorphosis.

From 1976 to 1979 Reppert was a postdoctoral fellow in neuroendocrinology at the National Institute of Child Health and Human Development in Bethesda, Maryland, in David C. Klein's laboratory, which focuses on the pineal gland and circadian biology.

Reppert and colleagues discovered that the two mouse cryptochromes, mCRY1 and mCRY2, function as the primary transcriptional repressors of clock gene expression, and the mPER proteins are necessary for CRY nuclear translocation.

[12] This work provided the first portrayal of a negative transcriptional feedback loop as the major gear driving the mouse molecular clock.

[13] Reppert and colleagues found that the core mechanisms for the SCN in mammals consist of interacting positive and negative transcriptional feedback loops.

[27][28] Each fall, millions of monarchs from the eastern United States and southeastern Canada migrate as much as 4,000 km to overwinter in roosts in Central Mexico.

Reppert and colleagues have focused on a novel circadian clock mechanism and its role in time-compensated sun compass orientation, a major navigational strategy that butterflies use during their fall migration.

As presented in a review article,[28] the clock mechanism, on a gene/protein level, operates as follows: Reppert’s lab expanded upon Fred Urquhart's postulation that antennae play a role in monarch migration.

[33] Reppert's lab also studied antennae in vitro and found that antennal clocks can be directly entrained by light and can function independently from the brain.

"[34] In 2013, Reppert and Patrick Guerra showed that spring remigrants also use an antenna-dependent time-compensated sun compass to direct their northward flight from Mexico to the southern United States.

[36] Reppert and colleagues Patrick Guerra and Robert Gegear showed that migratory monarchs can use a light-dependent, inclination-based, magnetic compass for navigation on overcast days.

[37] Genetic studies from Christine Merlin’s laboratory show that the photoreceptive CRY1 protein is essential for the monarch’s light-sensitive magnetic compass.

[38] The successful use of reverse genetics in monarchs would indicate that the butterfly is an excellent choice for helping to delineate the molecular mechanism underlying light-dependent magnetosensing in the context of compass navigation.

Reppert and Patrick Guerra showed that fall migrants prematurely exposed to overwintering-like coldness reverse their flight orientation to the north.

The temperature microenvironment at the overwintering site is essential for successful completion of the migration cycle: without cold exposure, aged migrants continue to orient to the south.

The discovery that coldness triggers the northward flight direction in spring remigrants underscores how vulnerable the migration may be to climate change.

[44] In 2013, Christine Merlin and Scot Wolfe developed in Reppert’s lab a novel gene-targeting approach in monarchs that uses a zinc finger nuclease strategy to define the essential nature of CRY2 for clockwork function in lepidopterans.

[46] In 2016, Reppert collaborated with Marcus Kronforst at the University of Chicago and others to use population genetic studies to define the evolutionary history of the monarch migration.