Rules valid until 31-dec-1999:

1.3.012: The point of the saddle shall be a minimum of 5 cm to the rear of a vertical plane passing through the lower bracket spindle. The saddle support shall be horizontal (see figure 1). The length of the saddle shall be 24 cm minimum and 27.5 cm maximum.
.
1.03.13: The maximum height of the hand support point shall be level with or below a horizontal line passing through the horizontal plane of the saddle top. This point of support may not be situated behind the axis of the steering column.
The overall length [forward projection] of the handlebars may not exceed a limit set 15 cm for-ward
of a vertical line passing through the front wheel spindle.

1.03.15: The distance between the vertical passing through the lower bracket spindle and the front wheel spindle (AB) shall be between 54 cm minimum (1) and 65 cm maximum.
The distance between the vertical passing through the lower bracket spindle and the rear wheel spindle (AC) shall be between 35 cm minimum and 50 cm maximum.

1.03.18:
1. With regard to the distances of 15 and 65 cm stipulated in articles 1.3.013 and 1.3.015, until 31st December 1999 a different of these distances shall be tolerated but the total distance must not go beyond 80 cm.

New rules starting 1-jan-2000:
1.03.22:
In races other than those covered by article 1.3.023, only the traditional type of handlebars (see diagram “handlebars”) may be used. The point of support for the hands must be positioned in an
area defined as follows: above, by the horizontal plane of the point of support of the saddle (B);
below, by the horizontal line passing through the highest point of the two wheels (these being of
equal diameter) (C); at the rear by the axis of the steerer tube (D) and at the front by a vertical line
passing through the front wheel spindle with a 5 cm tolerance (see diagram “Structure (1)”). The
distance referred to in point (A) is not applicable to the bicycle of a rider who takes part in a sprint,
keirin or Olympic sprint race, but must not exceed 10 cm in relation to the vertical line passing
through the front wheel spindle.

1.03.23:
For individual time trials and time trials for teams of up to four riders on the road, and for the individual and team pursuits, kilometre and 500 m time trials and record attempts on the track, an extension may be added to the steering system. The overall length of this section may not project beyond a point 10 cm in front of a vertical line passing through the front wheel spindle (AA), with the other limits set in article 1.3.022 (B,C,D) remaining unchanged. A support for the elbows or forearms is permitted (see diagram “Structure (1)”).
For individual road time trials and time trials for teams of up to four riders, controls or levers fixed to
the handlebar extension may extend beyond the 10 cm limit as long as they do not constitute a
change of use, particularly that of providing an alternative hand position beyond the 10 cm mark.

This effects just the aerodynamic position. But there are new rules regarding the frame design, which effect severely the whole bike industry, since only standard frame designs are allowed anymore. (Hey, but you are allowed to use oval tubes!)
Forget the german FES designs, GT superbikes, Zipps, Softrides, etc....
All the exciting carbon frame designs will pass away, thanks to the UCI. This is the first time in sport history that officials have the power to stop the natural evolution of a fascinating sport and put it back 20 years...

1.3.022:
In races other than those covered by article 1.3.023, only the traditional type of handlebars (see diagram “structure 1”) may be used. The point of support for the hands must be positioned in an area defined as follows: above, by the horizontal plane of the point of support of the saddle (B);below, by the horizontal line passing through the highest point of the two wheels (these being of equal diameter) (C); at the rear by the axis of the steerer tube (D) and at the front by a vertical line passing through the front wheel spindle with a 5 cm tolerance (see diagram “Structure (1A)”). The distance referred to in point (A) is not applicable to the bicycle of a rider who takes part in a sprint, keirin or Olympic sprint race, but must not exceed 10 cm in relation to the vertical line passing
through the front wheel spindle.
The brake controls attached to the handlebars shall consist of two supports with levers. It must be possible to operate the brakes by pulling on the levers with the hands on the lever supports. Any extension to or reconfiguration of the supports to enable an alternative use is prohibited. A combined
system of brake and gear controls is authorised.

1.03.023
For time trials and for the individual and team pursuits, kilometre and 500m time trials, an extension may be added to the steering system. The distance between the vertical line passing through the bottom bracket axle and the extremity of the handlebar may not exceed 75 cm, with the other limits set in article 1.3.022 (B,C,D) remaining unchanged. A support for the elbows or forearms is permitted (see diagram “Structure (1B)”).
For road time trials, controls or levers fixed to the handlebar extension may extend beyond the 75 cm limit as long as they do not constitute a change of use, particularly that of providing an alter-native hand position beyond the 75 cm mark.
For the track and road events covered by the first paragraph, the distance of 75 cm may be increased to 80 cm to the extent that this is required for morphological reasons; “morphological reasons”should be taken as meaning anything regarding the size or length of the rider’s body parts. A
rider who, for this reason, considers that he needs to make use of a distance between 75 and 80 cm must inform the Commissaires’ Panel at the moment that he presents his licence. In such cases the Commissaires’ Panel may carry out the following test: ensuring that the angle between the forearm and upper arm does not exceed 120° when the rider is in a racing position.
(amendment came into force 7th June 2000).