Points of Concurrency in Triangles

What are the centroid, the incenter, the circumcenter, and the orthocenter of a triangle?[br][br]How do the points of concurrency in triangles help solve problems?[br][br]Does the centroid always lie inside the triangle?[br]Does the incenter always lie inside the triangle?[br]Does the circumcenter always lie inside the triangle?[br]Does the orthocenter always lie inside the triangle?[br]Can these points ever coincide?