I will discuss Z/2-equivariant motivic spectra. As an example, I will talk about a Z/2-equivariant motivic spectrum representing Karoubi's Hermitian K-theory, and my joint solution with Kriz and Ormsby of Thomason's homotopy limit problem. As another example, I will talk about motivic Hermitian cobordism, and its topological realization, topological Hermitian cobordism. This is an RO(G)-graded (Z/2 \times Z/2)-equivariant spectrum, whose RO(G)-graded homotopy groups we have computed.