We have exploited angle-resolved photoelectron spectroscopy (ARPES) to study the electronic structure of single crystal samples of high T-c material Bi2Sr2CaCu2O8+delta and of the antiferromagnetic insulator Sr2CuO2Cl2. As one moves away from optimal doping into underdoped region (T-c as low as 30K), the large Fermi surface sheet centered around the (pi,pi) point evolves into a small pocket centered around (pi/2,pi/2), and the saddle-point van Hove singularity is lost This evolution can be extrapolated to Sr2CuO2Cl2, which is apparently well described by the mean field spin-density wave calculation.