The universe was a very dark place in the first tens of millions of years before any luminous structure had formed. This epoch is sometimes referred to as the "Dark Ages", when dark matter (DM) collapsed into bound objects but hosted no stars whatsoever. These DM halos collected a primordial mix of primarily hydrogen and helium in their potential wells after they reached the cosmological Jeans mass MJ ~ 5 × 103 [(1 + z) / 10]3/2 . The first DM halos to cool and collapse produced the first stars in the universe that, in turn, produced the first metals to spark the transition to galaxy formation. Before reviewing the current status of research on the first stars and galaxies, it is worthwhile to step back, pose three simple but informative questions, and review historical pieces of literature that addressed these questions.
The first question we can ask ourselves is: Why do all observed stars contain metals?  focused on the Milky Way (MW) stellar population and observed (i) that the oldest Population II stars were metal-poor, (ii) a high frequency of white dwarfs, and (iii) a red excess in elliptical galaxies. These points led them to the conclusion that the "original Population II contained a large number of relatively massive stars".
The next question that naturally follows is: Without any metals, how does gas cool and condense to form stars? Metal-enriched gas cools mainly through H2 formation on dust grains and other fine-structure transitions in heavy elements.  recognized that H2 can slowly form in the gas phase through the following reactions:
or less efficiently
 were the first to realize that H2 formation in the gas-phase was important in star formation in the early universe. They used these reactions to determine that H2 cooling dominates the collapse of a pre-galactic cloud at number densities n > 104 cm-3. These high density regions can cool to ~ 300 K and continue to collapse.  suggested that globular clusters were the first bound objects in the universe with masses ~ 5 × 105 M. In their calculations, they first compute the properties of these objects from linear perturbation theory and then follow the initial contraction of the cloud, including H2 cooling. They find that molecular hydrogen cooling is indeed efficient enough to drive a free-fall collapse, in which only a small fraction of the total gas mass forms stars due to the inside-out nature of the collapse.
The third pertinent question is: When and where do the first stars form? Applying the properties of cooling primordial gas to the cold dark matter model,  determined that the first objects to cool and collapse due to H2 formation would be hosted in DM halos with masses ~ 106 M at z = 20-30. A decade later,  used a detailed chemical model to follow the formation of H2 in virialized objects, starting from recombination. They found that the redshift-dependent minimum DM halo mass to host H2 cooling, rising from 5 × 103 M at z ~ 100 to 106 M at z ~ 15.
These early analytical works provided the theoretical basis for current and recent simulations that focus on the formation of the first stars and galaxies in the universe. Here I review the progress that the field has made in the past decade.