I will present different methods and theoretical models on the detection of the first stars, which play a crucial role in galaxy formation, but which have not yet been observed.

The first stars, which are believed to be more massive than present-day stars, might be indirectly observable by the gravitational wave emission of the merger of their compact remnants. I present our self-consistent, semi-analytical model to simulate the formation of the first stars and compare our estimates for the detection rates with aLIGO to other recent estimates.

Pair-instability supernovae (PISNe) are very energetic explosions of massive, metal-poor stars, which are observable up to high redshift. I will discuss the optimal survey strategy to find PISNe from the first stars with JWST. We maximise the visibility time of the PISN lightcurves per invested exposure time with NIRcam. Short exposures of <1ks with the right filters are sufficient to reliably select PISN candidates for a follow-up observation to confirm their transient nature.

I will also review Galactic archaeology as a third, fundamentally different approach to observe the first stars indirectly. If the interstellar medium out of which the second generation of stars formed got enriched by exactly one previous supernovae, we can observe this characteristic chemical fingerprint in the abundance of extremely low-metallicity stars in the Milky Way. Connecting stellar archeology surveys to models of the Milky Way assembly enables us to identify the most promising regions to find these second generations of stars and to determine their progenitor masses.