Let me take a deep breath, because this is not an simple topic to broach. Since I've started shooting with my Canon 6D, and based on the recommendations of many of you, I've been saving all my photos to both JPEG and RAW formats. My mirrorless camera also could save RAW images, but I never really used it for numerous reasons. Primarily because I was already accustomed to my workflow for quickly posting photos to accompany stories on the site, partly for file storage and management considerations, but also because I knew that adopting a RAW workflow would require both new software and knowledge of new image processing techniques. I simply wasn't ready to tread those deep waters.
But took the dive I did, and just like the jump from an APS-C-sized sensor camera to a full frame one, it's difficult to see myself going back. Processing photos is a lot of fun, and even therapeutic. So here's what I've learned from dabbling in RAW photo processing for two months, which just skims the surface of what you can do with a RAW file that you can't do with a JPEG.
A RAW file, unlike a JPEG, is not an image file in the traditional sense. It's not a single standardized file-type that you can open with any image editor or web browser--each camera company and even individual camera models store RAW data differently. Instead of the file denoting the color values of individual pixels, a camera's outputted RAW file encompasses all the light data captured by a camera sensor run through that camera's image processor. Data from different parts of the color spectrum aren't combined and flattened with luminosity settings--that's to be done on your computer. And so special RAW photo software is needed to process that data into a visual image, and lets you tweak that data to manipulate the final image.
But just as different cameras store RAW data slightly differently, RAW photo editing software have different algorithms in their engines to interpret that data. Adobe's Lightroom and Apple's Aperture will read RAW files in their own way before giving you an image to work with. That's not hugely consequential since all RAW editing software will let you tweak in myriad ways to eventually get your desired result, but it's important to remember that not all RAW converters are created equal. Some are favored for speed, some for compatibility with software suites, and some for unique features like direct camera tethering.
In my case, I chose to start with Adobe Lightroom 4, which is one of the more popular RAW converters. I chose it because it's cross platform (I image edit mostly on my Windows desktop), and because Adobe dropped the price of Lightroom significantly last year with the version 4 release. Even without an educational discount, you can find it for around $160, and I've seen it drop to below $100 during holiday sales. If you favor another RAW editor, please share why you like it in the comments!
Lightroom 4 isn't just a RAW photo editor, it's also a very good file manager. The first thing that happens when you plug in a camera or memory card is the import process, which transfers photos (both RAW and JPEG) to the directory of your choosing. As a file manager, Lightroom has many sorting and tagging options. I have it automatically file photos away according to date taken, and then create groups based on events for processing. In tests conducted by DPreview, Lightroom 4 wasn't as fast as some other RAW editors to import photos, but that's because the software also creates high-resolution thumbnails for each image in the library, which are also customizable. Imports can take several minutes for a few dozen photos, but the ability to instantly preview thousands of photos in high-resolution makes it worth it.
This is also a good place to point out that an SSD is extremely useful for RAW processing. I originally had my photos stored on a 1TB hard disk drive, but the software chugged when calling up 25MB file after file to edit. Now I keep my Lightroom library on a 256GB SSD.