"Writing on dirty paper" refers to the communication problem over a channel with both noise and interference, where the interference is known to the encoder non-causally and unknown to the decoder. This problem is regarded as a basic building block in communication, and it has been extensively investigated by Costa and other researchers. However, little is known in the case that the encoder can have access to feedback from the decoder. In this paper, we study the dirty paper coding problem for feedback Gaussian channels without or with memory. We provide the most power efficient coding schemes for this problem, i.e., the schemes achieve lossless interference cancelation. These schemes are based on the Kalman filtering algorithm, extend the Schalkwijk-Kailath feedback codes, have low complexity and a doubly exponential reliability function, and reveal the interconnections among information, control, and estimation over dirty paper channels with feedback. This research may be found useful to, for example, power-constrained sensor network communication.