  We study interference channels (IFC) where interaction among sources and
destinations is enabled, e.g., both sources and destinations can talk to each
other using full-duplex radios. The interaction can come in two ways: 1) {\em
In-band interaction:} sources and destinations can transmit and listen in the
same channel simultaneously, enabling interaction. 2) {\em out-of-band
interaction:} destinations talk back to the sources on an out-of-band channel,
possible from white-space channels. The flexibility afforded by interaction
among sources and destinations allows for the derivation of interference
alignment (IA) strategies that have desirable "engineering properties":
insensitivity to the rationality or irrationality of channel parameters, small
block lengths and finite SNR operations. We show that for several classes of
interference channels the interactive interference alignment scheme can achieve
the optimal degrees of freedom. In particular, we show the {\em first simple
scheme} (having finite block length, for channels having no diversity) for
$K=3,4$ that can achieve the optimal degrees of freedom of $\frac{K}{2}$ even
after accounting for the cost of interaction. We also give simulation results
on the finite SNR performance of interactive alignment under some settings.
  On the technical side, we show using a Gr\"{o}bner basis argument that in a
general network potentially utilizing cooperation and feedback, the optimal
degrees of freedom under linear schemes of a fixed block length is the same for
channel coefficients with probability 1. Furthermore, a numerical method to
estimate this value is also presented. These tools have potentially wider
utility in studying other wireless networks as well.
