  We overview recent developments in the study of alignment hydrodynamics,
driven by a general class of symmetric communication kernels. A main question
of interest is to characterize the emergent behavior of such systems, which we
quantify in terms of the spectral gap of a weighted Laplacian associated with
the alignment operator. Our spectral analysis of energy fluctuation covers both
long-range and short-range kernels and does not require thermal equilibrium (no
closure for the pressure). In particular, in the prototypical case of
metric-based short-range kernels, the spectral gap admits a lower-bound
expressed in terms of the discrete Fourier coefficients of the radial kernel,
which enables us to quantify an emerging flocking behavior for non-vacuous
solutions. These large-time behavior results apply as long as the solutions
remain smooth. It is known that global smooth solutions exist in one and two
spatial dimensions, subject to sub-critical initial data. We settle the
question for arbitrary dimension, obtaining non-trivial initial threshold
conditions which guarantee existence of multiD global smooth solutions.
