Points of Concurrency in Triangles

What are the centroid, the incenter, the circumcenter, and the orthocenter of a triangle?[br][br]How can the centroid 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 all be in one place?