How to wrap text around an irregular shape or cut-out photo
Layout by Zaweba wraps text by contour using detected edges, an alpha channel or a path, with per-side offsets, invert and jump options.

Select the picture or shape in Layout by Zaweba, open text wrap and choose a contour wrap instead of the bounding box. The contour can come from the picture's detected edges, from its alpha channel or from a path, and an offset keeps the text a comfortable distance away. Text in any frame behind it then flows around the outline of the subject rather than around a rectangle.
Wrapping text around a cut-out figure, a product or a curvy illustration is one of the things that makes a magazine page look designed rather than assembled. It is also easy to overdo, so a little care goes a long way.
Choosing where the outline comes from
Detected edges work on pictures with a clear subject against a plain background, such as a product shot on white. Layout finds the edge and builds the wrap from it.
Alpha channel is the choice when the picture already has transparency, such as a PNG or a layered PSD with the background removed. The transparent areas define the outline exactly, so the wrap follows the cut-out precisely.
A path gives you full control. Draw a path or use the shape itself, and the wrap follows it. This suits illustrations, shapes you have drawn on the page, and any case where the automatic outline isn't quite what you want.
Other wrap options
Bounding box is still the right choice for most rectangular pictures. Jump object stops text on either side, so it only appears above and below. Jump to next column sends the text on to the next column once it reaches the object. Invert wraps text inside the shape rather than around it. Offsets can be set per side, so you can give more room on the side where the text runs close.
Doing it well
Give the wrap enough offset. Text that runs right up to an edge looks cramped and is harder to read. Look at the result at actual size, not zoomed out.
Watch the ragged edge. Justified text wrapping around a curve can produce very short lines with wide gaps. Tweaking the offset, or letting the text near the shape run ranged left, often helps. A line of one or two words beside a curve is usually a sign the wrap is too tight or the shape too deep into the column.
Keep the wrap simple on dense pages. A wrap around a single strong cut-out is striking. Several on one page tend to make the text hard to follow.
Related tools
Clipping paths, set by detected edges or alpha, control what part of the picture shows, while the text wrap controls where the text goes. They often use the same outline but they are separate settings, so check both. The fitting options and crop decide how the picture sits in its frame before either comes into play.
For text inside a shape rather than around it, a shape or polygon frame can be used as a text frame, and shapes can be converted to frames. Combined with a contour wrap on a neighbouring cut-out, that gives you magazine-style pages without any tricks.
If the wrap misbehaves
If text doesn't wrap at all, check that the wrap is set on the picture or shape itself, since that is where the setting lives. If the outline is rough, try the alpha channel or a drawn path instead of detected edges. If a wrap leaves a stray word stranded on the far side of a shape, a slightly larger offset or jump object on that side usually cures it.