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We characterize the capacity region to within 2 bits/s/Hz and the symmetric capacity to within 1 bit/s/Hz for the two-user Gaussian interference channel (IC) with feedback. We develop achievable schemes and derive a new outer bound to arrive at this conclusion. One consequence of the result is that feedback provides multiplicative gain at high signal-to-noise ratio: the gain becomes arbitrarily large for certain channel parameters. This finding is in contrast to point-to-point and multiple-access channels where feedback provides no gain and only bounded additive gain respectively. The result makes use of a linear deterministic model to provide insights into the Gaussian channel. This deterministic model is a special case of the El Gamal-Costa deterministic model and as a side-generalization, we establish the exact feedback capacity region of this general class of deterministic ICs.