Several outstanding problems in the research of magnetic cataclysmic variable binaries (mCVs) are reviewed. Magnetic cataclysmic variables are divided into the high magnetic field strength (10-230 MG) polars and the intermediate magnetic field strength (0.01 - 10 MG) intermediate polars (IPs). Current problems in polar and intermediate polar research are much the same as those from the foundation of the field and include (1) the long-term orbital period evolution, in particular testing of the disrupted magnetic breaking hypothesis for the formation of the upper edge of the CV period gap, (2) the origin of high and low luminosity/accretion states, (3) the structure white dwarf magnetic field, dipolar or complex and (4) the origin of radio emission in mCVs and measuring the donor magnetic fields. These issues are interconnected in complex ways. Some historical context is given and a summary of the state of progress towards solutions is presented.