I review the results and techniques used by the MIT H-up arrow group t
o achieve a fractional resolution of 2 parts in 10(12) in the 1S-2S tr
ansition in hydrogen [1]. With some improvements, this system should d
eliver 100 times higher resolution with an improved signal count rate
getting us closer to an old advertised goal of a precision of 1 part i
n 10(18). While these developments are very important for the proposed
test of the CPT theorem through the comparison with anti-hydrogen, so
me of the techniques used with hydrogen are not applicable to anti-hyd
rogen and I discuss some difficulties and alternatives for-the trappin
g and spectroscopy of anti-hydrogen.