There are about 20,000 species of Platyhelminthes, most of them parasitic. All flatworms are acoelomate, triploblastic and bilaterally symmetrical.
    The flatworms are the simplest animals with bilateral symmetry and three distinct germ layers, yet their tissues are specialized for various functions, and two or more types of cell tissues may combine to form organs.  Unlike most other bilaterally symmetrical animals, the flatworms have a digestive cavity with only one opening.  Since the animals cannot feed, digest, and eliminate undigested residues simultaneously, food cannot be processed continually.
    Flatworms have solid bodies, with no circulatory system for the transport of oxygen and food molecules, so all cells must be within diffusion distance of sources of oxygen and food.  Their body structure is well suited to fulfilling these requirements.  The body is flattened, which keeps the cells close to the external oxygen supply.  Also, the digestive cavity is branched, carrying food particles to all regions of the body.
    About 13,000 species of flatworms have been described, and they are placed in three classes:  class Turbellaria, which contains mostly free-living (nonparasitic) forms; class Trematoda, encompassing parasitic flukes; and class Cestoda, with tapeworms (also parasitic).

Class Turbellaria

The free-living (non-parasitic) flatworms form a large and varied group.  Turbellarians are predominately free-living and aquatic. They have an incomplete digestive tract, in which the mouth leads to a pharynx, then to temporary spaces containing cells that take in food particles by phagocytosis. Digestion is intracellular. These animals move by laying down slime from special skin glands, then gliding along these "slime trails" by the beating of epidermal cilia.

    Turbellarians are mostly carnivorous, preying on tiny invertebrates that they locate by means of their chemoreceptors. They are a diverse group, including over 4500 known species divided into twelve orders.

Class Trematoda

All trematodes are parasitic, and most adult trematodes parasitize vertebrates. Around 9000 species have been described. Their body is covered with a tegument, a peculiar kind of epidermal arrangement in which the main cell bodies are deep, separated from the cytoplasm that lies next to the exterior by a layer of muscle (but connected to the exterior layer by cellular processes.  The tegument lacks cilia in adults.  Trematodes are characterized by one or two suckers or hooks on their anterior ends by which they fasten onto their victims. They are like turbellarians in having a relatively well developed alimentary canal, and their muscular, excretory, and reproductive systems are also relatively complete.

Most trematodes have complex life cycles, with larval stages parasitizing one or more species that are different from host of adults.  Most trematodes are endoparasites (parasites which live inside the host's body). They include several parasites that have an enormous impact on human populations, such as human liver flukes and the blood flukes that cause schistosomiasis.  The symptoms of schistosomiasis are caused by the eggs, which have sharp spines on the surface and are laid in the capillaries of the bladder wall or intestines.  The eggs lodge in the liver and spleen, blocking blood vessels, and their sharp spines tear the surrounding tissues, causing hemorrhages.  Schistosomiasis now affects some 200 to 300 million people in 71 countries in Asia, Africa, and South America.

Class Cestoda

The cestodes, or tapeworms, differ in a number of ways from other flatworms. Their bodies are long and flat, made up of many segments called proglottids. Each proglottid is a reproductive unit, essentially a factory to produce gametes.  Cestodes' teguments are covered with tiny projections, microvilli, which increase its surface area and thereby increase its ability to absorb nutrients from a host. Digestive tracts are absent completely, and tapeworms also lack mouths and digestive enzymes. At the tapeworm's anterior end is a specialized segment called a scolex, which is usually covered with hooks or suckers and serves to anchor it to the host.  The tapeworms merely hang on and absorb predigested food molecules through their skin.

Tapeworms are found in the intestines of many vertebrates, including humans, and may grow as long as five or six meters.  They cause illness not only by encroaching on the food supply but also by producing wastes and by obstructing the intestinal tract.  The most common human tapeworm, the beef tapeworm, infects people who eat the undercooked flesh of cattle that have grazed on land contaminated by human feces containing tapeworm segments.
    All of the 5000 or so known species of tapeworms are endoparasites. Most require at least two hosts, with the host of the adult tapeworm a vertebrate. Intermediate hosts are often invertebrates. A number of tapeworm species inhabit humans.
 

Thanks so much to these extremely helpful sites for the information and/or pictures they provided!  Check them out for even more in depth information, pictures, and essays.
 

http://animaldiversity.ummz.umich.edu/platyhelminthes.html

http://www.sidwell.edu/us/science/vlb5/Labs/Classification_Lab/Eukarya/Animalia/Platyhelminthes/

http://biology.unm.edu/biology/bio404/Platyhelminthes.html