The most crucial immediate challenge, for both observers and theorists, is to close the gap between the mass scale accessible to ab initio simulations (virial masses of ~ 108 M), and to cutting-edge observations (inferred total masses of ~ 1010 M). We have encountered this fundamental problem repeatedly in our preceeding discussion. A second key need is to derive better predictions for the number counts of the first galaxies, and to devise robust multi-color and spectroscopic criteria to disentange the likely mix of Pop III and Pop II stars, possibly together with an AGN component, encountered in the first galaxies. The appearance of the first galaxies in sub-millimeter to radio bands needs to be explored theoretically. In particular, atomic and molecular lines such as CII and CO lines may be promising in detecting and characterizing the first galaxies (Walter & Carilli 2007; Obreschkow et al. 2009). Finally, to fully harness the tremendous potential of stellar archaeology in local dwarf galaxies, a much increased sample of high-quality elemental abundances is needed.
The study of the first galaxies enters an exciting period, where advances in supercomputer technology enable ever more realistic ab initio simulations within a realistic cosmological context. This is matched by equally exciting prospects on the observational side, where next-generation facilities - such as JWST, the planned 30-40m extremely large telescopes on the ground, ALMA, and the SKA - will finally open up the high-redshift frontier. It is very likely that if another review on the first galaxies is written a decade from now, our understanding of the subject will have completely changed. This again reflects the special stage this field is in, where we are just at the threshold of a golden age of discovery.
The authors thank Andrew Benson, Andrea Ferrara, Zoltan Haiman, Adam Lidz, Masami Ouchi, and John Wise for carefully reading earlier drafts of the present review and also for providing comments. V.B. is supported by the National Science Foundation grant AST-1009928, and by NASA through Astrophysics Theory and Fundamental Physics Program grants NNX08-AL43G and NNX09-AJ33G. N.Y. acknowledges support from the Grants-in-Aid for Young Scientists (S) 20674003 by the Japan Society for the Promotion of Science and from World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan.