  The LCDM cosmological model is a well defined, simple and predictive model
which is consistent with the majority of current cosmological observations.
Despite of these successes there are specific cosmological observations which
differ from the predictions of LCDM at a level of 2\sigma or higher. These
observations include the following: 1. Large Scale Velocity Flows (LCDM
predicts significantly smaller amplitude and scale of flows than what
observations indicate), 2. Brightness of Type Ia Supernovae (SnIa) at High
Redshift z (LCDM predicts fainter SnIa at High z), 3. Emptiness of Voids (LCDM
predicts more dwarf or irregular galaxies in voids than observed), 4. Profiles
of Cluster Haloes (LCDM predicts shallow low concentration and density profiles
in contrast to observations which indicate denser high concentration cluster
haloes) 5. Profiles of Galaxy Haloes (LCDM predicts halo mass profiles with
cuspy cores and low outer density while lensing and dynamical observations
indicate a central core of constant density and a flattish high dark mass
density outer profile), 6. Sizable Population of Disk Galaxies (LCDM predicts a
smaller fraction of disk galaxies due to recent mergers expected to disrupt
cold rotationally supported disks). Even though the origin of some of the above
challenges may be astrophysical or related to dark matter properties, it should
be stressed that even on galactic and cluster scales, the effects of dark
energy on the equilibrium and stability of astrophysical systems are not
negligible and they may play a key role in the resolution of the above puzzles.
Here, I briefly review these six challenges of LCDM and discuss the possible
dark energy properties required for their resolution.

Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory