  [abridged] With their long mean free paths and efficient heating of the
intergalactic medium (IGM), X-rays could have a dramatic impact on the thermal
and ionization history of the Universe. We explore this in various signals: (i)
Reionization history: including X-rays results in an earlier, more extended
reionization. Efficient thermal feedback from X-ray heating could yield an
extended, ~10% ionized epoch. (ii) Reionization morphology: a sizable (~10%)
contribution of X-rays to reionization results in a more uniform morphology,
though the impact is modest when compared at the same global neutral fraction,
xH. However, changes in morphology cannot be countered by increasing the bias
of the ionizing sources, making them a robust signature. (iii) The kinetic
Sunyaev-Zel'dovich (kSZ) effect: at a fixed reionization history, X-rays
decrease the kSZ power at l=3000 by ~0.5 microK^2. Our extreme model in which
X-rays dominate reionization is the only one that is marginally consistent with
upper limits from the South Pole Telescope, assuming no thermal
Sunyaev-Zel'dovich (tSZ) - dusty galaxy correlation. Since this extreme model
is unlikely, we conclude that there should be a sizable tSZ-dusty galaxy
signal. (iv) The cosmic 21cm signal: the impact of X-rays on the 21cm power
spectrum during the advanced stages of reionization (xH<0.7) is modest, except
in extreme, X-ray dominated models. The largest impact of X-rays is to govern
IGM heating. In fact, unless thermal feedback is efficient, the epoch of X-ray
heating likely overlaps with the beginning of reionization (xH>0.9). This
results in a 21cm power spectrum which is ~ 10-100 times higher than obtained
from naive estimates ignoring this overlap. However, if thermal feedback is
efficient, the resulting extended epoch between X-ray heating and reionization
could provide a clean probe of the matter power spectrum in emission.
