  Originally introduced in connection with general relativistic Coriolis
forces, the term $\textit{frame-dragging}$ is associated today with a plethora
of effects related to the off-diagonal element of the metric tensor. It is also
frequently the subject of misconceptions leading to incorrect predictions, even
of nonexistent effects. We show that there are three different levels of
frame-dragging corresponding to three distinct gravitomagnetic objects:
gravitomagnetic potential 1-form, field, and tidal tensor, whose effects are
independent, and sometimes opposing. It is seen that, from the two analogies
commonly employed, the analogy with magnetism holds strong where it applies,
whereas the fluid-dragging analogy (albeit of some use, qualitatively, in the
first level) is, in general, misleading. Common misconceptions (such as
viscous-type "body-dragging") are debunked. Applications considered include
rotating cylinders (Lewis-Weyl metrics), Kerr, Kerr-Newman and Kerr-dS
spacetimes, black holes surrounded by disks/rings, and binary systems.
