We review how the 6.5 meter James Webb Space Telescope (JWST) --- after its launch planned for 2018 --- can measure the epochs of First Light, Reionization, and Galaxy Assembly, building on recent results from the Hubble Wide Field Camera 3. Significant technical progress has been made on the design and fabrication of JWST: more than 80% of its launch mass has been built, passed final design, or is being built as of Spring 2013. All JWST's 18 flight mirrors have been gold-coated with an optical performance that meets or exceed specs. Two of JWST's scientific instruments were delivered to NASA GSFC in 2012, with the last two to follow in 2013.
We show what combination of area, depth, and wavelength coverage are needed for JWST to detect a sufficient number of First Light objects, and to measure their evolving luminosity function (LF). JWST will map the epoch of First Light through Pop III-star dominated objects at redshifts z=8--20, and its transition to the first Pop II stars in dwarf galaxies at z<9. JWST will measure the evolution of the steep faint-end of the dwarf galaxy LF at z=6--15, which likely provided the UV-flux needed to start and finish cosmic Reionization.
I will also discuss: 1) simulations of deep JWST images, using lower redshift restframe UV--optical HST images as templates; (2) if ultradeep JWST images will run into the instrumental or natural confusion limits; (3) to what extent gravitational lensing bias from foreground object halos may affect the search for First Light objects at redshifts z>8--10. A new generation of algorithms may be needed to automatically detect, measure and classify objects in very crowded, ultradeep JWST fields; and (4) the optimum mix of random deep JWST fields, and lensing fields centered on foreground clusters or groups.