  The supersymmetry preserving mu parameter in SUSY theories is naively
expected to be of order the Planck scale while phenomenology requires it to be
of order the weak scale. This is the famous SUSY mu problem. Its solution
involves two steps: 1. first forbid mu, perhaps via some symmetry, and then 2.
re-generate it of order the scale of soft SUSY breaking terms. However, present
LHC limits suggest the soft breaking scale m_{soft} lies in the multi-TeV
regime whilst naturalness requires mu~ m_{W,Z,h}~ 100 GeV so that a Little
Hierarchy (LH) appears with mu << m_{soft}. We review twenty previously devised
solutions to the SUSY mu problem and re-evaluate them in light of whether they
are apt to support the LH. We organize the twenty solutions according to: 1.
solutions from supergravity/superstring constructions, 2. extended MSSM
solutions, 3. solutions from an extra local U(1)' and 4. solutions involving
Peccei-Quinn (PQ) symmetry and axions. Early solutions would invoke a global
Peccei-Quinn symmetry to forbid the mu term while relating the mu solution to
solving the strong CP problem via the axion. We discuss the gravity-safety
issue pertaining to global symmetries and the movement instead toward local
gauge symmetries or R-symmetries, either continuous or discrete. At present,
discrete R-symmetries of order M (Z_M^R) which emerge as remnants of Lorentz
symmetry of compact dimensions seem favored. Even so, a wide variety of
regenerative mechanisms are possible, some of which relate to other issues such
as the strong CP problem or the generation of neutrino masses. We also discuss
the issue of experimental verification or falsifiability of various solutions
to the mu problem. Almost all solutions seem able to accommodate the LH.
