We present a detailed investigation of the Cepheid distance scale by using both theory and observations. Through the use of pulsation models for fundamental mode Cepheids, we found that the slope of the period-luminosity (P-L) relation covering the entire period range (0.40<=logP<=2.0) becomes steeper when moving from optical to near-infrared (NIR) bands, and that the metallicity dependence of the slope decreases from the B- to the K band. The sign of the metallicity dependence for the slopes of the P-LV and P-LI relation is at odds with some recent empirical estimates. We determined new homogeneous estimates of V- and I-band slopes for 87 independent Cepheid data sets belonging to 48 external galaxies with nebular oxygen abundance 7.5<=12+log(O/H)<=8.9. We investigated the dependence of the period-Wesenheit (P-W) relations on the metal content and we found that the slopes of optical and NIR P-W relations in external galaxies are similar to the slopes of Large Magellanic Cloud (LMC) Cepheids. They also agree with the theoretical predictions suggesting that the slopes of the P-W relations are independent of the metal content.