So, what are they? They are filters (glass or resin) that are placed in front of the lens elements to alter the exposure in some way. There are many different types, but the most common types are solid neutral density and graduated neutral density filters. There are also reverse graduated neutral density filters, but we'll discuss those later. They can be the screw on type, or they can be plate filters (typically in 100x100mm - 4x4in and 100x150mm - 4x6in).
What are they for? The solid filters are for extending exposures... that is to say, they limit the amount of light over the whole image, allowing you to take longer exposures. You can take 4 minute exposures in full sun! Or use a wide aperture (1.8? 1.4?) in full sun! There are many different types. 1 stop, 2 stop, 3 stop, 4 stop, 6 stop, 10 stop, etc. Lee makes whats called the big stopper (10 stops of light reduction) and the little stopper (6 stops of light reduction). I have both the big and little stopper. The split filters, or graduated neutral density filters, are for reducing the exposure in one section of the image. The top is "dark," and the bottom is clear. They come in soft transition (the transition between dark and clear is gentle), and hard transition (the transition between dark and clear is almost a perfect line). They are often used in areas where the sky is much brighter than the foreground. This means you need to "darken" part of it, but leave the rest "clear." This will make more sense later when I post examples.
Now... What do I choose? How do I know which ones are for me? I started out with the LEE system.. YES, it's very expensive. But, I figured with good quality filters and holders, I'll never have to replace them unless I break one. So I decided thus. Other companies commonly talked about are Cokin, Hi-Tech, Singh-Ray, and B+W. But Lee and Cokin are the two most common in terms of holders.
Next, we need to decide which filters to get. I picked up the LEE holder, a wide angle adapter (it sets the holder closer to the lens, and thus reduces vignetting at wide angles). I first started with a set of 3 soft graduated neutral density filters (100x150mm, 4x6in). 1, 2, and 3 stops. That is to say, the top cuts three stops of light, and the bottom doesn't. Why the soft edge? It is more versatile, and used for landscapes where the horizon is not perfect. Hard edged transitions are designed for shots where the horizon is a neat line, like the water. I then added a big stopper (10 stops, 100x100mm, 4x4in). Then a Little Stopper (6 stops, 100x100mm, 4x4in). Then a reverse graduated neutral density filter of 2 stops (darkest in the middle, hard edged transition, lighter again towards the top, 100x150mm, 4x6in), and now a set of hard edged GND's. Most recently I added a Landscape Circular Polarizer, and the 105mm front-accessory ring to my kit.
Now on to examples.
Here's what the filters look like (left is hard-edged, right is soft edged).
And here they are mounted on a D800. The ability to rotate and move the filters for fine adjustment is what makes them incredibly versatile and significantly better than the screw-in style filters.
Below is the system modified to fit the landscape polarizer--for ultra-wide shots (I.E. 16mm on full-frame) I use a 77mm wide-angle adapter, the foundation kit with 2 filter slots and the 105mm front-accessory ring, and the landscape polarizer mounted on that ring. With that setup, I can achieve minimal to almost no vignetting, and this setup can hold the polarizer and 2 plate filters.
Here is an unedited image, with no filters whatsoever.
And here's the same scene with a 2-stop reverse graduated neutral density.
The top has no filters, and the bottom has a 2 stop and 3 stop graduated neutral density soft edged filter. Just look at that second histogram!
Now, what happens when we approach a scene that requires filters? How does it look from start-to-finish? See the gallery below for the progression of unfiltered to final image (hover over each image to see what filters are applied).
And now for some proper examples. Hover over the image to see what filters were used.
Filters help in many ways, and allow creativity and ingenuity that would not be allowed without them. That being said, filters aren't always the best option. To this day I still use HDR and tone-mapping in some scenes. If you have any questions, please drop them in the comments below and I'll do my best to answer all of them!