The history and evolution of reversed phase stationary phases in described in detail in an article by Majors, Dolan, Carr and Snyder. 
In the 1970s, most liquid chromatography runs were performed using solid particles as the stationary phases, made of unmodified silica gel or alumina. This type of technique is now referred to as normal-phase chromatography.  Since the stationary phase is hydrophilic in this technique, and the mobile phase is non-polar (consisting of organic solvents such as hexane and heptane), biomolecules with hydrophilic properties in the sample adsorb to the stationary phase strongly. Moreover, they were not dissolved easily in the mobile phase solvents. At the same time hydrophobic molecules experience less affinity to the polar stationary phase, and elute through it early with not enough retention. This was the reasons why during the 1970s the silica based particles were treated with hydrocarbons, immobilized or bonded on their surface, and the mobile phases were switched to aqueous and polar in nature, to accommodate biomedical substances.  
The use of a hydrophobic stationary phase and polar mobile phases is essentially the reverse of normal phase chromatography, since the polarity of the mobile and stationary phases have been inverted – hence the term reversed-phase chromatography. As a result, hydrophobic molecules in the polar mobile phase tend to adsorb to the hydrophobic stationary phase, and hydrophilic molecules in the sample pass through the column and are eluted first. Hydrophobic molecules can be eluted from the column by decreasing the polarity of the mobile phase using an organic (non-polar) solvent, which reduces hydrophobic interactions.  The more hydrophobic the molecule, the more strongly it will bind to the stationary phase, and the higher the concentration of organic solvent that will be required to elute the molecule.
Many of the mathematical parameters of the theory of chromatography and experimental considerations used in other chromatographic methods apply to RP-LC as well (for example, the selectivity factor, chromatographic resolution, plate count, etc. It can be used for the separation of a wide variety of molecules. It is typically used for separation of proteins, because the organic solvents used in normal-phase chromatography can denature many proteins.  
Today, RP-LC is a frequently used analytical technique. There are huge variety of stationary phases available for use in RP-LC, allowing great flexibility in the development of the separation methods.