The digital mirrorless camera is a new category, but has become a success. Digital mirroless cameras have become popular because they offer DSLR-like image quality, handling, and features, while being smaller and lighter system. 

Instead of DSLR's optical viewfinders, mirrorless cameras have an electronic viewfinder (EVF) that gives a digital preview of how the image will be recorded by the camera. That is why they can be so compact and light.

The thing about changing your camera: Most camera diehards will have invested in lenses and accessories for their camara. Choosing for different type of camera means doing all that effort (and expenditure) all over again.

The best mirrorless camera overall: Fujifilm X-T1 (great viewfinder, 16-MP APS-C sensor for crisp, detailed images, great manual focus, rugged, weather-sealed body, attractive, retro design, pro-level performance)

The second best mirrorless camera: Olympus OM-D E-M1 (built-in image stabilization)

The best compact mirroless camera: Olympus PEN-F (great for street photography)