Standard filters, on digital cameras
Filters used to be part and parcel of doing photography. Color correction was a big deal. It’s still a big deal. Wratten filters to adjust for lights, and lighting. When one goes deep into a canyon to shoot a waterfall, the light’s not “white”. The mind’s eye automatically corrects. The camera can correct too.
So we don’t carry 81A, or 81B, no more magenta to attempt correction for the green shifts in fluorescent lights. The kit is smaller, and lighter and that’s pretty good. If you make a mistake (shooting cloudy for sun, or flash for tungsten) you can correct in Lightroom, or Photoshop, or LightZone; whatever your preference happens to be.
This doesn’t mean filters are dead. Forget the “effects” filters, such as stars, and rainbows, those are what they are, and if they are useful to you, there is no replacement. But other, of the, “basic” filters from days of yore, are still as useful as they ever were.
Why? What is it they provide which the applications don’t?
Let’s look under the hood, again. Camera’s trap light. How they trap light is the difference between one and another. Back in the “old days” the big difference was the lenses, and accessories. The medium in which the light was caught was the same from camera to camera. Film was the medium, and it was continuous. 
When the process of photography was first discovered the films weren’t sensitive to the full spectrum of light. As time went on, the chemistry of emulsions was improved, from orthographic, to panchromatic (adding green and red, respectively), until the entire spectrum was there. The layering of the emulsions meant every square nanometer was sensitive to all the light.
Digital cameras are not continuous. Each pixel is sensitive to one spectrum of light, red, green, or blue (unless you have an Olympus, but it’s not relevant to this). Part of the processing time from the shutter to “done writing” is the math to convert the pixel colors to visual colors
B&W has always been a bit different, yet again. Once the tricks of collecting the entire spectrum were solved, the depth and contrast of the entire scene could be captured (look at early photos, and part of the softness is the lenses, and some of it is because the emulsions couldn’t catch all the light). If a bit of light hits the emulsion, it activates a bit of silver. The more light, the more silver is activated, and the lighter that area will become.
To shoot B&W with digital the information is a lot more complicated. First a map of individual spots of RGB has to be made. Then it has to be converted to color, then that color map has to be reduced to a grayscale image. Instead of a direct relationship, we have an approximation.
But some colors are about as reflective as other colors. The raw quantity of light they reflect is about the same, which means they record much the same on the film. To fix that, to make one thing darker than the other, we use filters. Because a filter absorbs the light in the same spectrum a red filter will make red subjects lighter. It also has the effect of making the opposite side (i.e. green, with a red filter) of the spectrum darker (I think this is because it absorbs the lesser amount of light on from the opposite side of the spectrum being reflected. In this regard it parallels the effect of a polarising filter).
Will this work, when one takes all the steps involved into account? Will the effect be worth the trouble? You have to judge that for yourself. I shot a series of a tree stump, with a series of filters. Red, Green, Blue, Orange and Yellow Polarising. The Yellow Polarising I added to the other four.
The first shot was done in color, and converted to B&W in Lightzone. The only other thing done was a moderate sharpening. I did exactly the same thing to all the rest.
As shot, simple conversion.
With a Blue Filter
This one with an Orange.
There are differences. (it’s easier to see them if you open them in tabs, and cycle from tab to tab). If we look at the original image, we can see the oranges, browns, white, grays, greens, and blues. We can also see those areas in the grays of the monochrome images. The different filters restrict different wavelengths of light, which gives the variation in the final product.
If you want to do it, what do you need? Filters. Either the “ring” type, which screw into the front of the lens, or the “square” type, which slide into a holder (which is attached to the front of the lens in some way). I prefer the square type, because 1: They are cheaper (without any real difference in quality), and 2: most systems (I use Cokin) allow for “stacking” them, and 3: they allow for the use of “graduated” filters.
The first thing to remember is that, as with all filters, they steal light. In terms of metering this doesn’t mean much, but darker filters (such as red) will require either a faster ISO, or a tripod.
The second thing (which becomes obvious the moment you look through the lens) is that things look different.
Becomes this one
That’s what red, with a yellow polariser, looks like, without correction. The details are hidden. This is another of the reasons I like square filters. I can frame the scene before I put the filter in place. Focusing through dark filters is problematic. Either set the focus first, or trust the autofocus.
When you process it, it becomes:
All the detail is still there; even if it’s too compressed into the red spectrum for the human eye to resolve, the sensor (and the film) can.
The last thing to keep in mind is the meter. Autofocus won’t be usually be fooled by the filter, but the meter will usually underexpose the image. I don’t know why (logically the expectation would be the darker scene will be overexposed, but experience tells me this is not the case). It’s going to be some trial and error, because each meter is different, and there is no way to know how much it’s been fooled until you look at the conversion to black and white.
Continuous, when speaking of film, means the tones are evenly graded, from the blackest color the silver in the paper can produce, to the brightest white. Since the way in which the silver interferes with the clear flow of light allows for some refractive bending there are no sudden shifts. This is why photos (even color ones) photo-copy so badly; they are being converted from continuous medium, to a non-continuous one. It took the discovery of half-tone conversions to make it possible to use photographs in newspapers, which is why the US Civil War was illustrated with drawings.