The Cepheid method to determine the distances to spiral galaxies,
and its principal sources of systematic error, is reviewed. I will
report on the work of our Araucaria Project group to reduce the 
most serious systematic uncertainty in the method, the distance
of the Large Magellanic Cloud, to 2% using late-type eclipsing binaries
consisting of two giant components. I will also briefly discuss
the physical properties of a unique classical Cepheid in one of these
LMC systems, and show that the classical Cepheid mass discrepancy
problem has finally been solved with this star. I will describe the
Araucaria project method to determine very accurate Cepheid distances
to nearby galaxies using combined optical and near-infrared photometry,
and demonstrate that the effect of metallicity on near-infrared
Cepheid period-luminosity relations is very small and consistent with
zero.