  We analyze, via Imry-Ma scaling arguments, the strong disorder phases that
exist in low dimensions at all temperatures for directed polymers and
interfaces in random media. For the uncorrelated Gaussian disorder, we obtain
that the optimal strategy for the polymer in dimension $1+d$ with $0<d<2$
involves at the same time (i) a confinement in a favorable tube of radius $R_S
\sim L^{\nu_S}$ with $\nu_S=1/(4-d)<1/2$ (ii) a superdiffusive behavior $R \sim
L^{\nu}$ with $\nu=(3-d)/(4-d)>1/2$ for the wandering of the best favorable
tube available. The corresponding free-energy then scales as $F \sim
L^{\omega}$ with $\omega=2 \nu-1$ and the left tail of the probability
distribution involves a stretched exponential of exponent $\eta= (4-d)/2$.
These results generalize the well known exact exponents $\nu=2/3$, $\omega=1/3$
and $\eta=3/2$ in $d=1$, where the subleading transverse length $R_S \sim
L^{1/3}$ is known as the typical distance between two replicas in the Bethe
Ansatz wave function. We then extend our approach to correlated disorder in
transverse directions with exponent $\alpha$ and/or to manifolds in dimension
$D+d=d_{t}$ with $0<D<2$. The strategy of being both confined and
superdiffusive is still optimal for decaying correlations ($\alpha<0$), whereas
it is not for growing correlations ($\alpha>0$). In particular, for an
interface of dimension $(d_t-1)$ in a space of total dimension $5/3<d_t<3$ with
random-bond disorder, our approach yields the confinement exponent $\nu_S =
(d_t-1)(3-d_t)/(5d_t-7)$. Finally, we study the exponents in the presence of an
algebraic tail $1/V^{1+\mu}$ in the disorder distribution, and obtain various
regimes in the $(\mu,d)$ plane.
