Newtonians (also known as catoptrics) usually use a concave parabolic primary mirror to collect and focus incoming light onto a flat secondary (diagonal) mirror that in turn reflects the image out of an opening at the side of the main tube and into the eyepiece.

 

Advantages
 
Lowest cost per inch of aperture compared to refractors and Catadioptrics since mirrors can be produced at less cost than lenses in medium to large apertures.
Reasonably compact and portable up to focal lengths of 1000mm.
Excellent for faint deep sky objects such as remote galaxies, nebulae and star clusters due to the generally fast focal ratios (f/4 to f/8).
Reasonably good for lunar and planetary work.
Good for deep sky astrophotography (but not as convenient and more difficult to use than Catadioptrics).
Low in optical aberrations and deliver very bright images.
 
Disadvantages
 
Generally not suited for terrestrial applications.
Slight light loss due to secondary (diagonal) obstruction when compared with refractors.