In traditional film photography, infrared is photographed using a combination of infrared sensitive film and external infrared filters. Because of the characteristics of the external filter, slow shutter speeds and tripods were a necessity. The resulting photographs would be rendered as monochromatic (B&W).
In digital photography, there is no film involved and infrared can be photographed with an external filter as in film, or by having the internal sensor filter replaced with an infrared friendly filter. The advantage of having the internal filter replaced is that unlike using an external filter, normal shutter speeds can be used. The disadvatage of this path is that the camera becomes a dedicated infrared camera.
The filter I selected to have installed in my DSLR is an R72 type filter. This filter does let in some visible light, allowing a slight color cast, called false color, in the rendered photographs. This filter, in my opinion gives the best of both worlds: photographs with color cast or using photoshop to remove the color cast, B&W infrared photographs. The color cast can be controlled somewhat by bracketing exposures.
In the infrared photographs, biological greens are rendered as white/near white while the remainder of the photograph is rendered as B&W. All infrareds on this site were shot in bright sunlight during all seasons except winter.