  We analyze various aspects of the recently proposed holographic theories with
general dynamical critical exponent z and hyperscaling violation exponent
$\theta$. We first find the basic constraints on $z, \theta$ from the gravity
side, and compute the stress-energy tensor expectation values and scalar
two-point functions. Massive correlators exhibit a nontrivial exponential
behavior at long distances, controlled by $\theta$. At short distance, the
two-point functions become power-law, with a universal form for $\theta > 0$.
Next, the calculation of the holographic entanglement entropy reveals the
existence of novel phases which violate the area law. The entropy in these
phases has a behavior that interpolates between that of a Fermi surface and
that exhibited by systems with extensive entanglement entropy. Finally, we
describe microscopic embeddings of some $\theta \neq 0$ metrics into full
string theory models -- these metrics characterize large regions of the
parameter space of Dp-brane metrics for $p\neq 3$. For instance, the theory of
N D2-branes in IIA supergravity has z=1 and $\theta = -1/3$ over a wide range
of scales, at large $g_s N$.
