DADA was kind of this anti-art movement that started in the
early 20th century to protest the war and all of society's crazy
values. It eventually dissipated as it became popular and thus
pointless. Man Ray, Max Ernst, and Marcel Duchamp were all
considered part of this movement.
This led to SURREALISM which wanted to express images from the
subconscious. They looked at dreams and such. Dali and Picasso were
both part of this movement at one time. It was led by Andre
Breton.
Picasso started CUBISM with Georges Braque. Inspired by
primitive art, this movement changed the way we looked at painting
in general. It was more 2-D. They tried different techniques,
sometimes showing multiple perspectives in the same picture.
EXPRESSIONISM and THE FAUVES have also left their mark on art
history. They both used flat form and solid colors in their
painting, inspired by primitive art as well. The Fauves were a
pretty happy lot with Henri Matisse and Andre Derain as their
leaders. Expressionists were generally a little more dark, trying
to express their inner universes, a philosophy that carries on
today. They were inspired by Vincent van Gogh and Edvard Munch.
The FUTURISTs tried to portray movement in a still work of art.
There were also a variety of other art movements that came and left
with little mark on art history.
After World War II, ABSTRACT EXPRESSIONISM became very popular.
They may have been inspired by Wassily Kadinsky who's tried
painting music in the early 20th century. Jackson Pollock is who I
consider to be a leader of this movement.
To protest abstract expressionism, POP ART was born. It made art
out of common images of our lives. Very artificial and detached.
Rebellious, ironic, and funny. Andy Warhol is generally considered
one of the greatest pop artists of all time.
I really don't know what the heck POST-CONTEMPORARY or
POST-MODERN means. The Modern Movement is believed to be the whole
of all art movements between the beginning of the 20th century and
the end of WWII. It refers to a kind of thinking in art that the
academic art of the past should be rejected. Once again, I have no
clue how post-modern art can be identified as an actual way of
thinking about art. Some people believe post-modern means that we
can now look at old academic art and the modern art that protested
it and learn from both, but generally it seems post-modern artists
just continue the tradition of rejecting traditional art through
new methods like PERFORMANCE ART and LANDSCAPE ART.
Important art movements in the that have continued into the 21st
century are MINIMALISM (tried to strip down works to the
fundamental features--imagine a box...yeah), NEW CLASSICISM (pretty
much old renaissance like techniques with a modern setting),
CONCEPTUAL ART (asks the question "What is art?"), LOWBROW ART
(punk revolution meets the fine visual arts), and NEO-EXPRESSIONISM
(pretty much expressing inner emotions like the expressionist, but
with more modern techniques in painting).
A variety of people, inspired by the art movements of the 20th
century, try to create their own art movements. These movements
include THINKISM and OMNI ART and will only be mentioned in passing
in art history books if mentioned at all. (Which they probably
won't).
Anyway, I hope my extended answer will be of some help for
you.