It would be very hard to define what is literary fiction since the classification is very subjective but in general terms literary fiction is a written piece that is focused more on its style and in its language. In that way of categorizing things then, works that have become popular like bestsellers would not fall under the category of literary fiction. This means that most of today’s most popular works could not be considered to be literary fiction. Science fiction, chick lit, mystery, or horror can not be considered to be literary fiction although it would incorporate some elements of these genres into its content. Categorizing classic works like those of H.G. Wells or Jules Verne though would even be more difficult since they are considered to be pillars of world literature.
Today there are those who consider literary fiction to be just another genre like science fiction or mystery although it must be argued that as a genre it lacks the unifying quality that would mark all other types of fiction. Some authors like John Updike felt that the only reason that his works could be considered as literary fiction was because they were written in words and that it would be useless to define fiction as being literary or not. Mot of these writers fell that the term is being hyped up as a means of marketing by publishers.
There are works though that without a doubt would fall the category of literary fiction or literary novel. The final work of James Joyce, Finnegans Wake which is to ordinary people is a large rambling collection of random words and gibberish, actually is an attempt to remake the novel as we know it. It is a combination of free dream association, stream of consciousness writing, and allusions to other literary works. It has been largely unread by a public who fails to understand the significance of the work. Another work that can be considered as a literary work without any reservations is the monumental In Search of Lost Time by Marcel Proust. It is a mixture of all the literary possibilities in style and themes.
If you want to read the literary fiction today, you could try checking some of the anthologies that come out each year which offers a collection of the finest literary works to come out. It would be a great experience absorbing these great works of fiction.