There are many themes of both. So, here are some of the big ones. Many people in the modern era had a belief in the triumph of science and technology and the decline in religion. This is something that has not happened. People are more religious now than ever before. There was also a strong or naive view in meta-narratives in the modern era, such as continual progress for humanity, which does not exist in a post-modern era. Part of the decline in such a view is the two massive world wars. Postmodernism repudiates large scale narratives and challenges things authority.
I usually think about the modern and the postmodern as related but separate eras. Still, it's possible to see them as one era and to talk about some themes or concerns that they share. My comments focus entirely on literature, but it's possible to talk about other areas, too, such as architecture or the visual arts.
One possible theme is multiplicity. Rather then present the unified views of a small group of people, in a unified form, the modern and postmodern literary work often seeks to present a range of views in a range of forms. A 19th-century novel is often very nicely structured, and all of the plot lines are tied together and resolved before the work ends. Such a novel often opens with a clear setting, with names of characters, etc., before any dialogue begins. A modern or postmodern novel (e.g. Mumbo Jumbo) may often open in a jarring manner, may never answer the questions that it raises at the start, and may incoporate forms that don't normally belong in novels.
Another possible theme is interiority. The modern/postmodern didn't invent the idea of the inner self, of course, but modern and postmodern literature has taken interiority to a new level. Stream-of-consciousness is one example.
An important concept in postmodern perspective on language is the idea of "game". In the context of postmodernism, the game means changing the framework for connection of ideas, and thus allow the passage of a metaphor or figurative meanings or word from one context to another, or from a reference frame to another. As postmodern thought within the text is composed of a series of "markings" whose meaning is assigned to the reader, not the author, this game is based on the means by which the reader constructs or interprets the text, and with which the author becomes a presence in the reader's mind. The game involves invoking then and works written in the same manner to weaken their authority, or by parodying their assumptions or style, or by successive layers of erroneous indications regarding the author's intention.