Interesting question!
What exactly do you mean by "dark and gritty"?
There are a couple of quite different approaches, that come to my mind:
a) lighting - which could be low key with high contrast or dark pictures with less contrast.
Letting the audience more *guess*, than see...
Lighting your scenes carefully or chosing to just use available light...
b) camerawork - shaky handheld or almost steady pictures from a tripod
unconventional angles (very low / high / dutch...)
Documentary style vs. cinematic style...
c) editing - fast paced or very calm
d) postproduction: grading (adding colour / removing colour), chosing a special look (thinking of "Sin City", "Pitch Black", "7even" ...)
e) soundeffects and music will give a movie atmosphere that can hardly be achieved through visuals alone. Not to use any music will be a different approach
f) gear: what camera do you use. A movie filmed with a mini-DV will look totally differend than when using ... say a RED...
This is just some sort of brainstorming, what *can* be "dark and gritty".
Do you have any examples (films etc.) in mind?
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