Currently available data on the real, R-s, and imaginary, X-s, parts o
f the microwave frequency surface impedance Z(s) = R-s + iX(s) are pre
sented for high quality single-crystal high-temperature superconductor
s YBa2Cu3O6.95, Ba0.6K0.4BiO3, Tl2Ba2CaCu2O8-delta, Tl2Ba2CuO6+delta,
and Bi2Sr2CaCu2O8. A high-precision technique for measuring the temper
ature dependences R-s(T) and X-s(T) in the range 4.2 less than or equa
l to T less than or equal to 150 K is described. Surface impedance and
complex conductivity features common to single crystal high temperatu
re superconductors are formulated and the temperature variation of the
se properties is analyzed. To explain the experimental data, a modifie
d two-liquid model is used, which includes quasiparticle scattering an
d accounts for the characteristic change in the density of superconduc
ting carriers at low at near-critical temperatures. Prospects for the
microscopic theory of high frequency response of high-temperature supe
rconductors is discussed.