A Gaussian cognitive interference channel model with state is investigated, in which transmitters 1 and 2 communicate with receivers 1 and 2 via an interference channel. The two transmitters jointly send one message to receivers 1 and 2, and transmitter 2 also sends a separate message to receiver 2. The channel outputs at the two receivers are corrupted by an independent and identically distributed (i.i.d.) Gaussian state sequences and Gaussian noise variables. The state sequence is noncausally known at transmitter 2 only. The Gaussian channels are partitioned into two classes based on channel parameters. For each class, inner and outer bounds on the capacity region are derived, and either the partial boundary of the capacity region or capacity region is characterized for all Gaussian channels. The cognitive interference channel with state known at both transmitter 2 and receiver 2 is further studied, and the capacity region is established for a class of such channels. It is also shown that this capacity can be achieved by certain Gaussian channels with state noncausally known only at transmitter 2.