What are Vector Formats?
A Vector format is using mathematical equations of geometrical primitives such as points, lines, curves, and shapes or polygon's, to represent images in computer graphics.

Vector formats are different, yet complementary to raster graphics, which uses an array of pixels to construct the graphics, typically used with photographic image graphics. There are times when working with vector design tools and formats is the best option, whilst other times working with raster tools and formats is the best option. There are also times when vector and raster formats are used together. An understanding of both the advantages and limitations of each technology is most likely to result in efficient and effective use of the proper tools.

Computer displays are made up from grids containing small rectangular cells that are called pixels. The display output is built up from these type cells. The smaller and closer the cells are together, the better the quality of the output image, however it also means it's a bigger file needed to store the image output data. If the number of pixels remains the same, the size of each pixel will stretch and the image becomes grainy (pixellated) when enlarged.

Vector format files store the lines, paths, points, shapes and colors that make up a graphic as a mathematical formula. A vector design program uses the mathematical formula file to construct the screens output image, providing the best quality possible, given the screen resolution. The mathematical formula file determines where the dots that make up the vector graphic should be placed for the best results when rendering the output image on a display monitor. Since the vector formula file can produce a graphic scalable to any size and detail, the quality of the graphic is limited only by the resolution of the monitor, and the file size of vector data rendering the graphic stays the same. Printing a vector graphic to paper will usually give a sharper, cleaner, higher output than printing it to the screen but can use the same vector formula file.

Editing vector graphics
Vector design software is used for creating and editing vector graphics. The graphics can be easily edited by screen objects which are then saved & updated to the mathematical formula file. Vector tools in the software can be used to stretch, twist, and color object layers in the graphic, and these tools are generally provided to the user through the vector software user interface on your computer. It is possible to export the graphic as a bitmap/raster file or generate a bitmap of any size from the vector file for any web or media use that requires raster image formats.

The size of the rendered file will be based on the resolution required, but the size of the master vector formula file will always remain the same. It is easy to export from a vector file to an assortment of bitmap/raster file formats, but it is much more difficult to try and do the opposite, especially if editing is required. It's an advantage to export a graphic created from a vector source file as a bitmap/raster format, as your bitmap/raster images have a wide variety of uses on the web. However, once a file is converted from the vector to raster, it is likely to be larger in size, and it will no longer have the advantage of scalability without loss of quality. You will also lose the ability to edit individual parts of the graphic once its a raster image. The file size of a vector graphic will depend on the number of layers/elements in it.

Printing
Vector formats are the ideal choice for print projects. Since a vector graphic is made from a series of mathematical curves, points, and paths it will print very crisp and clear even when resized. For instance, one can print a vector logo on a small sheet of copy paper, and then enlarge the same vector logo to billboard size with no quality loss at all. A bitmap/raster image would blur or pixelate excessively if it were magnified from business card size to billboard size due to the pixels.

If we regard letters and numbers as part of images, then the same rules apply even to the composition of written text for printing (typesetting). High quality print now days is based on fonts which are typically stored as vector files, and as such are scalable to any size without quality loss. Examples of these vector formats for fonts are "Postscript fonts" and "TrueType fonts".

Vector file extensions
There are many different softwares now days that can output and save as a pure 100% vector file. Print shops normally choose .Eps & .Ai over others.