Efficient and adapted frames are a useful tool for extracting information about curves, particularly upon examining a curve's image in a given frame. The Frenet frame is the classic example in R_3; however, Richard Bishop has introduced the other possible frame, which is suitable for more generally positioned curves. Our investigation will begin with identifying the four possible frames in R_4 and examining the relationships among them as well as some properties of certain curves' images. With this background we are prepared to state more general results about the images of curves with certain framings in R_n. In addition, the new concept of `branching' will be introduced with which the existence of 'simply branched frames' will be examined, and with which the possible efficient and adapted frames in R_n will be identified, labeled, and counted.