  There are two strong clues about the quantum structure of spacetime and the
gravitational dynamics, which are almost universally ignored in the
conventional approaches to quantize gravity. The first clue is that null
surfaces exhibit (observer dependent) thermal properties and possess a heat
density. This suggests that spacetime, like matter, has microscopic degrees of
freedom and its long wavelength limit should be described in thermodynamic
language and not in a geometric language. Second clue is related to the
existence of the cosmological constant. Its understanding from first principles
will require the dynamical principles of the theory to be invariant under the
shift $T^a_b \to T^a_b + (constant) \delta^a_b$. This puts strong constraints
on the nature of gravitational dynamics and excludes metric tensor as a
fundamental dynamical variable. In fact, these two clues are closely related to
each other. When the dynamical principles are recast, respecting the symmetry
$T^a_b \to T^a_b + (constant) \delta^a_b$, they automatically acquire a
thermodynamic interpretation related to the first clue. The first part of this
review provides a pedagogical introduction to thermal properties of the
horizons, including some novel derivations. The second part describes some
aspects of cosmological constant problem and the last part provides a
perspective on gravity which takes into account these principles.
