We discuss frustration effects by studying the two-dimensional Hubbard mode
l with nearest-neighbor(t) and next-nearest-neighbor(t') hoppings. We prese
nt results obtained by the mean-field solution, the exact diagonalization t
echnique, and the quantum Monte Carlo simulations. Questions to be addresse
d are: (1) magnetic phase diagram; (2) domain formation; and (3) supercondu
cting pair correlation functions.