Over time your masonry structure will get dirty. Whether it is growing mold or vegetation, in a polluted area where it takes on a blackish hue, gets covered with dirt or mud, exudes white runoff down its face, etc, masonry structures need to be kept up to date with a spring cleaning so to speak. They require maintenance like the rest of the known building structures. The type of appearance your structure takes on will determine the type of clean that you need. Most of the time, if the structure was built properly, you will just need to do a routine scrub or pressure washing of the structure. This will remove any greenery or vegetation type growth that will grow atop the masonry face along with any mold or dirt that might build up over time.
If there are stains left in the stone from the original build and sloppy use of mortar or concrete, or even from later repairs done to the structure, it might warrant a type of acid wash and scrubbing to remove all of the staining from the surface. With this type of stained covering it is never a guarantee of whether or not you will ever be able to remove it all. The problem with masonry type materials is that if another material is if left atop it and given time to absorb within it, it will penetrate deeper levels of the masonry lattice, making it much more difficult for a person cleaning to penetrate to the level that requires cleaning. If you encounter this kind of situation you might have to remove an area that is compromised and replace it, or remove some excess material to find a clean face in the material.
If you encounter a situation where you get white crystalline runoff down the face of your masonry you are observing a phenomenon known as efflorescence. When this occurs it usually has to do with the buildings intrinsic design. Masonry structures need to be built in accordance with how water moves in the area it is built. If water is trapped behind the masonry structure with no way to escape it will build up hydro-static pressure behind the structure. Where there is a water pressure gradient from one side of a masonry structure to the other, the water forces out salts and mineral deposits that are in the area and within the masonry structure themselves outward. So what we then experience are white runoff deposits on the faces of our masonry structure. To combat this, proper drainage should be added. There should be a drainage area behind you structure leading to “weep holes” in the front of you structure to allow water to pass through uninhibited. This will prevent the buildup of water pressure from behind you masonry structure. Once the water is given a place to go, you can remove the efflorescence buildup using a basic method of scrubbing or pressure washing, and if this doesn’t work you can resort to an acid wash.