In general, the molecules are presented in some kind of perspective drawing, based on the idea that the four substituents of a tetrahedral center can be divided into two pairs, laying in mutually perpendicular planes.  Most often the center and two of such substituents are shown in the plane of the drawing (i.e. the plane of the drawing surface) and their bonds are depicted as plain lines ( ––– ). 

Bonds to the other two substituents are shown with different symbols.  Bonds to atoms above the plane of the drawing (coming out, toward the viewer) are shown with a bold wedge (  ), with the narrow end of the wedge starting at the center.  As an alternative bold bonds (  ) are occasionally used.

Bonds to atoms below the plane (going in, away from the viewer) are shown with hash wedges (  ).  There are two separate conventions in use.  In the American usage the narrow edge points to the central atom, while in the European convention, the wide edge points to the central atom.  As an alternative, a set of short parallel lines ( ) is occasionally used.  A broken line () or an open wedge (  ) can also be found in some drawings, but their usage is discouraged.

These various presentations are illustrated below on an example of a compound with one stereocenter (in all cases the same S absolute stereochemistry is shown). The first structure (A) is the favored presentation, while B shows a rotational variant of A (any rotation within the plane of drawing is perfectly acceptable). Structure C demonstrates the European convention that has a more consistent perspective view of the wedges.  Structure D shows the use of open wedge (not recommended), while structure E illustrates the use of non-wedge bonds, that are commonly employed to designate relative stereochemistry (see below).

In addition to structures with two bonds to the stereocenter in the plane of the drawing (above), some representations may have only one bond in that plane (F and G) and some have none (H and I), as shown below.  In structures like F and G or H and I, three or four wedged lines are used to designate the 3D disposition of substituents,  respectively.

Confusingly, one may often encounter other 3D structures that seem to follow the above conventions, but are in fact different perspective representations. In structures J–M below, the plain bonds (–––) are not in the plane of the drawing. Their 3D disposition is implied by the wedge lines present.  For example, in structure J the wedge bond is a mast pole on three legs, and in L and M the plain-line bonds are really going in (in L) or out (in M) of the plane of the drawing.

Paying attention to the correct representation of the perspective is crucial.  Some incorrect usage of wedge bonds is illustrated in structures N and O.  Despite appearances, there is no stereochemical information in such structures.   A couple of simple rules can be used to decide adequacy of such drawings:  (1) the bold-wedge and the hash-wedge substituents must be on the same side of an imaginary line connecting the plain-line bonded substituents  (as in structures A or B), and  (2) two bold-wedge subsituents (or two hash-wedge substituents) must be on the opposite sides of an imaginary line connecting the plain-line bonded substituents (as in structures L or M).

Another way to present stereo-centers is with help of Fischer projections which are designed not to employ any wedged lines. The convention used is that all vertical bonds are pointing in, away from the viewer, and all horizontal bonds are pointing out, toward the viewer. Such structures can only have vertical and horizontal bonds on stereocenters, and cannot be rotated by 90° (without a change in stereochemistry).  Often, the most oxidized carbon is placed at the top (but other arrangements are acceptable as well). 

Structure P (above) is the Fischer projection, and it could be translated into a "wedge" structure H (or structures L or M, above).  One has to be careful to distinguish Fischer projections, such as P, from structures where no stereochemistry is explicitly shown, i.e. only plain bonds are used (in such cases 90° angles between drawn bonds should be avoided; see also below). 

Hydrogen atoms attached to the stereocenter are often not shown explicitly, as is common for skeletal structures. If done carefully, the omission does not lead to complications and the stereo information is perfectly readable, but there are instances where ambiguity or loss of stereo information may occur. In general, it is advisable to show stereocenter hydrogens explicitly. 

These structures, labeled with the same letters as their originals above, illustrate clear and unambiguous examples of hydrogens omitted without any loss of stereochemical information.  Structure P' is fine as long as it is made clear that it is a Fischer projection.  On the other hand, other presentations may be questionable.

For example, structure S can be interpreted (correctly) as structure L with hydrogen omitted, but (especially) when drawn by hand it may be interpreted as a poorly drawn structure of R, leading to the opposite 3D information.  Despite appearances, structure T does not carry any stereochemical information (the position of hydrogen with its plain-line bond needs to be explicitly specified). 

If stereochemistry is unspecified, no wedge lines are used, as in structure U. To easily distinguish such situation from Fischer projections, multiple 90° and 180° angles between drawn bond should be avoided. Alternatively, situations when the stereochemistry is unknown, or a mixture of both enantiomers is present, can be indicated explicitly by a wavy line ()  as shown in structure W.  Similarly,  the unspecified stereochemistry of the double bond (E or Z) may be shown by drawing "extended" formulas as in structure X.  The wavy line in structure Y is an alternative way to indicate unknown stereochemistry or a mixture of isomers.

For molecules with multiple stereocenters the plain-line bonds should be used to connect the centers, as illustrated for structure Z.  This approach avoids possible ambiguities as to which wedge bond belongs to each center.

As illustrated by structures Z' and Z" omitting stereocenter's hydrogens (if done properly) often increases the clarity of the presentation. Structure Z' with the wedge bonds designate absolute stereochemistry, i.e. enantiomerically pure compound with two S centers. Structure Z", with its constant-width lines, designates only the relative stereochemistry, i.e. it corresponds to the mixture of  (S,S) and (R,R) enantiomers.