Let E/F and K/F be quadratic extensions of number fields, and let V be a skew-Hermitian space over E. The twisted Gan-Gross-Prasad conjecture considers the restriction of representations from the unitary group U(V_K) to U(V). We discuss the relative trace formula approach to the global twisted GGP conjecture, and prove it in the unramified case under some local assumptions. This is joint work with Weixiao Lu and Zhiyu Zhang.