Exif can contain metadata about title, author, etc
Exif (Exchangeable image file format) can contain authorship, copyright information:
The metadata tags defined in the Exif standard cover a broad spectrum:
- Date and time information
- Descriptions
- Copyright information
Exif metadata can be present in JPEG images, for example. There is a complete listing of Exif tags which is too long to include here, but you are probably interested in the ImageDescription, Artist (or XPAuthor) tags.
Alternatively, XMP (Extensible Metadata Platform) provides a standard for embedding metadata in a file in the form of XML including multiple image formats.
PNG images use a different format, but can also contain metadata:
PNG provides the tEXt, iTXt, and zTXt chunks for storing text strings associated with the image, such as an image description or copyright notice. Keywords are used to indicate what each text string represents. Any number of such text chunks may appear, and more than one with the same keyword is permitted.
GIF files can include metadata in a comment block (thanks A C for pointing that out) as standard. They could also include information in plain text or application-extension blocks.
For vector image files, SVGs are XML and so can include metadata via the <metadata>, <title> and <desc> elements. (thanks A C for reminding me about SVGs)
Many of these metadata listings will conform to the Dublin Core schema/vocabulary, which gives standardised naming for each of the elements, eg 'Contributor', 'Creator', 'Date', etc.
Other means of including data in image files
As pointed out in the comments, there are other ways of including metadata in image files. I would point out that these are not necessarily part of an official file format or specification, however.
Steganography is the method of concealing a message within a message. This is a general technique and not limited to image files; it can also be done in video files, audio files, even in a physical medium.
There are images given as examples, such as:
→ 
(credit to Cyp on English Wikipedia for both images)
Additionally, a signature and date could be added to the image to embed author and creation time, for example.
Of course, all of these examples affect the actual image data itself, to a greater or lesser extent, unlike extra information contained in tags or fields.
