Internal stellar magnetic fields are inaccessible to direct observations and little is known about their amplitude, geometry and evolution. I will discuss how strong magnetic fields in the cores of red giant stars can be identified with asteroseismology. The fields manifest themselves via depressed dipole stellar oscillation modes, which arises from a magnetic greenhouse effect that scatters and traps oscillation mode energy within the core of the star. The Kepler satellite has already observed hundreds of red giants with depressed dipole modes, which can be identified as stars with strongly magnetized cores. Field strengths larger than roughly 10^5 G can produce the observed depression, and in one case a core field strength of 10^7 G can be measured. Strong core fields are present in roughly 50% of stars above 1.5 solar masses, suggesting that long-lived convective core dynamo-generated fields are common within these stars. Strong core fields are nearly absent in stars less than 1.2 solar masses, indicating that Sun-like stars do not harbor strong fields within their cores.