Except for the anarchistic Dada, everything that defines art to this day has been invented in the second half of the 19th century. Within five decades the art traveled a longer distance than in the five previous centuries. For the first time artists have fully realized their very condition; that not only the world of material and spiritual substance but also the projections of their mind and soul could be subjects of art. The search for a new world order and a new hierarchy of values created a couple of attitude constructs represented by three main trends in art: the Realism, the Symbolism and the Expressionism.
The second half of the 19th century was a period of brisk development of the science: caused by the Technological Revolution, the urbanization, the new classes of hired hands (proletariat) and the escalation of serious social conflicts.
By the end of the 18th century environmental sciences did not exist and, except for the philosophy, nor did the humanities, especially psychology and sociology. Even in the beginnings of the 19th century all these disciplines were being practiced in an amateur way. Theology, medicine, law and philosophy composed the scholarly quadrivium. It was thanks to the Technological Revolution which created the demand for pure research; the urbanization led to social conflicts solving of which required setting in order what was known about the society itself.
Philosophy was becoming dominated by Auguste Comte's (1798-1857) Positivism, originating from the Empiricism. It would not deny God; however, it would rather consider fruitless any attempt to explore the non-sensory reality. Simultaneously to Charles Darwin's (1809-1882) discoveries, Herbert Spencer (1820-1903) invented the Evolutionism (also called Social Darwinism): a variety of the biological determinism which deducted ethics from the theory of the struggle for life. Also connected with the Darwinism were the Naturalism and the philosophy of Karl Marx (1818-1883): the former, among others, represented by Ludwig Feuerbach (1804-1872), who denied the existence of all phenomena that wouldn't be emanations of matter; the latter developed popular by that time theory of social conflict (vide works of Ludwik Gumplowicz, 1838-1909, Polish sociologist and lawyer). However, it considered the defeat of one of the sides of conflict as the only possible solution.
The domination of the positivist materialism could not be balanced; not with isolated addresses of continuators of all sorts of the Idealism such as:
the opponent of natural sciences' attitude towards humanities Wilhelm Windelband (1848-1915),
English idealists – the father of the Transcendentalism Ralph Waldo Emerson (1803-1882);
Francis Herbert Bradley (1846-1924);
Franz Brentano (1838-1917), a psychologist, came up with the three classes of psychological phenomena: displays, judgments and emotional reflexes with the three ideals corresponding: beauty, truth and good. As during the Enlightenment, the theories formulated in England by the theoreticians of Gothic Revival, such as Augustus Pugin (1812-1852) and John Ruskin (1819-1900) remained outside of the field of continental disputes. Their accomplishments, or rather these of their heirs, changed the European art only at the end of the 19th century.
The man of the half 19th century could think whatever he or she wanted; they just did not know what could be the subject. He or she could be a scientist, a revolutionary, a philosopher, an inventor, even a motorcar's driver. He or she could even be happy: provided he or she did not bother with ultimate matters nor did search for the Absolute. And even if they did searched for it, they could not call it “God”. However an artist, provided they wanted to be more than
a mere decorator, must have searched for the Absolute and must have ask ultimate questions. Looking for an answer to these questions, the artist of the half of the 19th century remained alone. They were not supported any more by the already encrypted in culture, indisputable vision of transcendence. Even if an artist kept believing, the community feeling no longer supported them.
An example of the dilemma which had to be common for a number of sensitive people is Friedrich Nietzsche (1844-1900). Nietzsche ostentatiously rebelled against the Christian God which, according to him, was not worth any reverence since He was a forgiving God—and this would imply weakness. Only a God causing true religious fear could be real. A good psychologist would have probably explained easily what such a protest was a compensation for. Whatever the experience that created its basis—and this probably was Nietzsche's self-contempt for his “intellectual perfidy”—it brought Neitzsche's masterpiece Thus Spake Zarathustra: A Book for All and None, written in 1883 in which he announces the death of God and the birth of an Übermensch (Ger. “overman”). Even if, from a medical point of view, Nietzsche's opinions were a result of a deepening malfunction, from a human point of view they were a result of despair.
The art of the second half of the 19th century consisted of a few trends that continued the motifs of its predecessors.
The Positivist Realism was being developed by the Impressionism, the Neo-Impressionism and the post-impressionist paintings of Paul Cézanne.
The “idealistic” trend was being continued by the archaizing pre-Raphaelites, the Symbolism still including Christian traces, the paintings of Edvard Munch, the post-impressionist Pont-Aven school and the Post-Gauguin Les Nabis.
A proto-expressionist, multilayer, deeply symbolic Vincent van Gogh's work, as well as the actually already 20th century paintings of James Ensor were a total novelty in respect to the first half of the 19th century. 
The academic art is by far a completely separate topic in the 19th century's art; however, it has nothing to do with its themes or aesthetic values. It is rather about its obvious connections with philosophy, particularly  with the ontological and epistemological Realism. If for somebody a cold, philosophical terminology does not seem to be associated with beautiful Bouguereau's nymphs, it will be hard for them to understand fierce attacks against the academic art by former and contemporary heralds of modernity. The explanation can be found on the appropriate site of this domain.