The Erythrocytes AnatomyCredit: http://commons.wikimedia.org/wiki/File:Redbloodcells.jpg
We all know that the other name of erythrocytes is red blood cells. But did you know that erythrocytes are not true cells? Red blood cells lack nuclei or organelles, in which true cells have. 
Structural CharacteristicsAnatomy ErythrocytesCredit: http://commons.wikimedia.org/wiki/File:Erythrocyte_oxy.jpg
Red blood cells are small cells, shaped like a flattened disc with a depressed middle part. The color of RBC varies depending on the region; the edges have darker color compared to the center. To better understand the shape of RBCs, just picture a miniature doughnut. 
When erythrocytes mature, they are bound by a plasma membrane but they are anucleate. RBCs contain hemoglobin, the proteins that mainly functions during gas transport. Some other proteins, like antioxidant enzymes, are present in the RBCs. 
A special type of protein, called the spectrin, maintains the biconcave shape of the RBCs. The spectrin net adheres to the surface of the plasma member. Since the spectrin net can be deformed, it provides the RBCs the much needed flexibility. The erythrocytes are able to change its shape as it traverse the long and winding vessels of the body. With this capability, it is able to twist and turn when passing through capillaries which have diameters smaller compared to that of the erythrocytes. After passing thru these capillaries, the erythrocytes are then able to resume to its original, biconcave shape.  
Main Points to Consider
 Erythrocytes functionCredit: http://www.nanolab.com.ua/abstracts.html
The RBC is an excellent example of complementarity of function and structure. The unique shape of the erythrocytes greatly influences its gas transport function. The small size and doughnut shape present a huge surface area with relation to volume. Since the cytoplasm surrounds the erythrocyte, no point is far from the surface, making it ideal for gas exchange. Excluding the water components, an erythrocyte has over 97% hemoglobin. Hemoglobin is the molecule that respiratory gases bind to. It is also the transport vehicle for respiratory gases. Because erythrocytes are anucleate and generate its energy by way of anaerobic mechanism, they don’t have the appetite to consume the oxygen they are carrying, making them the ultimate carrier and transporter of oxygen. 
 Function of ErythrocytesCredit: http://emsbasics.com/2011/08/03/respiration-and-hemoglobin/
Erythrocytes know only one thing, and that is to act as gas transport vehicles. The red color of these cells is made possible by the hemoglobin, which easily binds with oxygen reversibly, meaning hemoglobin can bind with oxygen, and oxygen will bind with hemoglobin. The protein globin is the main component of hemoglobin and the heme pigment makes it red. Four polypeptide chains, two alpha and tow beta, compose the protein globin. The polypeptide chain is bound to the heme group. Within the heme group is an atom of iron which combines with one molecule of oxygen; therefore a single hemoglobin molecule is able to transport four oxygen molecules. This may sound not enough, but do consider that a single red blood cell carries with it 250 million molecules of hemoglobin. By doing a simple math, we can infer that a single red blood cell can carry almost 1 billion oxygen molecules.
 Anatomy of the ErythrocytesCredit: http://www.allvoices.com/contributed-news/8943283-the-blood
Since that hemoglobin is enclosed in erythrocytes as supposed to existing freely in the plasma, it prevents the hemoglobin from breaking down into fragments which may leak out into the bloodstream. It also prevents from influencing the viscosity of the blood and osmotic pressure. 
When oxygen binds to iron, it is now called oxyhemoglobin and the color changes to ruby red. As the RBC reaches its designated tissue, the oxygen detaches from the iron and the hemoglobin becomes dark red in color.