How to turn a photo into a vector halftone
Use Object > Image > Vector halftone in Vectornation by Zaweba to turn a photo into dots, squares, diamonds, ellipses or lines as real vector shapes.

A halftone dot pattern made of real vector shapes comes from one command in Vectornation by Zaweba. Place the photo, select it and choose Object > Image > Vector halftone. You choose dots, squares, diamonds, ellipses or lines, set a screen angle, and pick one ink, the image's own colours, or four CMYK screens. The result is vector artwork that stays sharp at any size.
Halftone is how printing shows shades of grey with one ink: bigger dots where the picture is dark, smaller ones where it is light. As a look, it suits posters, T shirts, comic style artwork and anything meant to feel printed.
Why vector halftone rather than a filter
A pixel halftone filter makes a picture of dots. It looks fine at the size you made it, but scale it up for a banner and the dots go soft. A vector halftone is a set of shapes, one per dot, so it can be enlarged as far as you like. It can also be recoloured, cut on a vinyl cutter, or separated onto a screen for printing, which a pixel version can't.
Step by step
Put the photo in your document with File > Place. Crop and size it roughly as you want the final artwork, because the halftone is built from the image as it sits on the page.
Select the image and choose Object > Image > Vector halftone. Pick a shape. Round dots are the classic newspaper look. Squares and diamonds feel more graphic. Ellipses give the soft chained look of older print. Lines turn the picture into rows of strokes that thicken and thin with the tone, which is striking on large pieces.
Set the screen angle. Angled screens look more natural to the eye than a straight grid; a 45 degree screen is the traditional choice for a single ink.
Then choose colour. One ink gives a single colour halftone, ideal for screen printing or a bold poster. The image's colours keeps the photo's hues with each dot coloured from the picture. Four CMYK screens builds cyan, magenta, yellow and black halftones at their own angles, like a printed magazine picture seen up close.
Getting a good result
The photo matters more than the settings. Strong contrast gives a clear halftone; a flat, grey photo turns into a field of similar sized dots with no picture in it. Adjust the photo in a picture editor before you bring it in if it needs more punch.
Keep dot size in proportion to the finished piece. Coarse dots read from across a room; fine dots read up close but can fill in on rough paper or fabric. A quick print at actual size will tell you more than the screen.
Very fine halftones produce a large number of shapes. That is fine for print, but if the file is getting slow, a coarser screen is lighter and often looks bolder anyway.
Taking it further
Because the result is ordinary vector artwork, the rest of Vectornation works on it. Recolour a one ink halftone with a spot colour from your colour books. Clip it inside a shape or lettering for a poster headline. Combine a line halftone with type for a record sleeve.
For screen printers, the CMYK option pairs well with Vectornation's separations preview, so you can check each plate before output. For one ink jobs, print or export the halftone as its own layer. If it's going to a cutter, export it in a format the cutter reads, such as DXF or HP-GL, though very small dots may be too fine to weed.
A vector halftone is one of those effects that looks complicated and turns out to be one menu command. Vectornation by Zaweba does it offline, as free software, with real shapes at the end.