  Strongly long-range interacting quantum systems---those with interactions
decaying as a power-law $1/r^{\alpha}$ in the distance $r$ on a $D$-dimensional
lattice for $\alpha\le D$---have received significant interest in recent years.
They are present in leading experimental platforms for quantum computation and
simulation, as well as in theoretical models of quantum information scrambling
and fast entanglement creation. Since no notion of locality is expected in such
systems, a general understanding of their dynamics is lacking. As a first step
towards rectifying this problem, we prove two new Lieb-Robinson-type bounds
that constrain the time for signaling and scrambling in strongly long-range
interacting systems, for which no tight bounds were previously known. Our first
bound applies to systems mappable to free-particle Hamiltonians with long-range
hopping, and is saturable for $\alpha\le D/2$. Our second bound pertains to
generic long-range interacting spin Hamiltonians, and leads to a tight lower
bound for the signaling time to extensive subsets of the system for all $\alpha
< D$. This result also lower-bounds the scrambling time, and suggests a path
towards achieving a tight scrambling bound that can prove the long-standing
fast scrambling conjecture.
