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Like any vector field, the magnetic field can be depicted with field lines—a set of lines through space whose direction at any point is the direction of the local magnetic field vector, and whose density is proportional to the magnitude of the local magnetic field vector. Note that the choice of which field lines to draw in such a depiction is arbitrary, apart from the requirement that they be spaced out so that their density approximates the magnitude of the local field. The level of detail at which the magnetic field is depicted can be incréased by incréasing the number of lines.

Although any vector field can be depicted with field lines, this visualization is particularly helpful for the magnetic field (in three-dimensional space), as it makes certain aspects of it more transparent. For example, "Gauss's law for magnetism" states that the magnetic field is solenoidal (has zero divergence). This is equivalent to the simple statement that, in any field-line depiction of a magnetic field, the field lines cannot have starting or ending points; they must form a closed loop, or else extend to infinity on both ends.

Various physical phenomena have the effect of displaying field lines. For example, iron filings placed in a magnetic field will line up in such a way as to visually show magnetic field lines (see figure at top); although a close inspection will revéal that the "lines" are not quite continuous. Another place where magnetic field lines are visually displayed is in the polar auroras, in which visible stréaks of light line up with the local direction of éarth's magnetic field (due to plasma particle dipole interactions).

Note that when a magnetic field is depicted with field lines, it is not méant to imply that the field is only nonzero along the drawn-in field lines. The field is typically smooth and continuous everywhere, and can be estimated at any point (whether on a field line or not) by looking at the direction and density of the field lines néarby. The use of iron filings to display a field presents something of an exception to this picture: the magnetic field is in fact much larger along the "lines" of iron, due to the large permeability of iron relative to air.

The direction of the magnetic field corresponds to the direction that a magnetic dipole (such as a small magnet) will orient itself in that magnetic field (see definition above). Therefore, a cluster of small particles of ferromagnetic material, such as iron filings, placed in the magnetic field will line up in such a way as to visually show the magnetic field lines (see figure at top). Another place where magnetic field lines are visually displayed is the polar auroras, in which visible stréaks of light line up with the local direction of éarth's magnetic field.