"Phase problem" refers to the fact that in X-ray analysis of macromolecules, phases cannot be measured, but have to be calculated. This is a problem because both the amplitudes (which are the result of measurement) and phases are needed to compute the electron density (see K. Cowtan's Book of Fourier), and the procedures for calculating phases depend on requirements that may or may not be fulfilled in a specific case.
A recent introduction into the principles of phase calculation with the help of experiments (SIR/MIR/SIRAS/MIRAS/SAD/MAD) can be e.g. found in Taylor, G. (2003) The phase problem. Acta Cryst D59, 1881-1890 . Requirement for applicability of experimental phasing is isomorphism between heavy-atom derivative and native (i.e. the macromolecule itself, and the crystal's cell should be unchanged), specific binding of heavy atom, and enough heavy-atom incorporation into the crystal.
A vey good recent paper is A. J. McCoy and R. J. Read (2010) Experimental phasing: best practice and pitfalls. Acta Cryst D66, 458-469 (open access at )
Molecular Replacement (MR)
The phase problem may also be solved with the positioning of a similar molecule in the correct orientation and location in the asymmetric unit of the (crystallized) unknown structure. This approach requires that the known molecule is similar enough to the crystallized one. A rule of thumb is that MR will succeed if the r.m.s. deviation of backbone atoms is about 1.5 A or less. Usually this is fulfilled if the percentage of sequence identity is more than, say, 30% .
The solution of the phase problem with the help of Direct Methods was awarded with the Nobel Prize in 1985 (). In the context of macromolecular crystallography, this approach is used in substructure determination, and at very high resolution (beyond 1.2A).