What is a Mirrorless?
A mirrorless camera is simply a striped down, compact version of a DSLR. There is obviously a mirror involved, but for this guide it really doesn't matter.
You have the same amount of control with either type of camera.
With that said I'll jump into the pros and cons of shooting with each type.
Size & Weight
The biggest difference between DSLRs and Mirrorless cameras is size and weight. Mirrorless cameras are much smaller and lighter than their DSLR counterparts. Due to the lack of some internal parts.
The Sony A7 II (Mirrorless) and the Canon 5D mk III (DSLR) are comparable cameras. Both shoot around 23 Megapixels, both have a full frame image sensor and both are professional level cameras. The Sony only weighs 556 g VS the Canon's 860 g. The Sony is also physically smaller making it much more compact and easier to carry.
Weight differences add up. With a lighter camera you can carry another lens or hike another mile further.
With a smaller camera comes a smaller battery. Mirrorless camera roughly get between 300-400 shots per battery, DSLRs come in around 600-800 shots. In addition to having a smaller battery, mirrorless cameras are always using theirs.
DSLRs, when not in live view mode, only use the battery for metering. So when you're looking through the viewfinder framing a shot you're not using any power.
Mirrorless don't operate that way. Since there is no mirror, the image sensor is always working to deliver you an image. Even if you're just framing up a shot.
Both types of cameras perform equally. There are both amazing DSLR and Mirrorless cameras. It comes down to your specific needs and what you're looking to shoot.
Lenses & Accessories
DSLRs have been around longer, so they have a much wider selection of lenses and accessories.
That's not to say mirrorless offerings aren't any good. Sony, Fuji, Olympus, and the rest simply don't have the selection of specialty lenses Canon or Nikon can offer.
This is a problem that will be solved with time. As Mirrorless cameras become more popular, there will be more accessories created for them.
Advantage: DSLR (For now)
Besides size and weight this is the biggest difference between the two types of cameras.
With a DSLR, when you look through the viewfinder the light is coming through your lens and into your eye.
With a mirrorless, when you look through the viewfinder you're looking at a small screen and the camera is displaying an image from the sensor.
A couple of years ago this could be a bit of a problem because the screens weren't that good. When you turned the camera to follow your subject you'd get lag as the camera took in the light and the displayed it on the screen. Today that problem doesn't exist.
With an electronic viewfinder you can display far more information than with a normal one. You also get to see exactly what you image will look like before you take it.
With some models you can even review your previous photo through the viewfinder if it's to bright to make out the image on the back screen.
Personally, I believe mirrorless cameras will replace DSLRs as the flagship camera for professionals and amateurs alike. The problem with mirrorless cameras are fixable. Batteries can be made more efficient and companies will make more lenses.
With all that said, I still shoot with a DSLR. I haven't made the switch, but every year it gets more tempting.
What kind of camera do you shoot with? Let me know in the comments below.