The stereochemistry of E1 and E1_CB is relatively easily to dissect. In terms of the first step the regiochemistry is reasonably clear (and there should be no stereochemistry to consider) - in E1_CB the most acidic proton (adjacent to the leaving group) is taken and in E1 the leaving group leaves! From the charged intermediate there are two possible olefinic outcomes and the more stable of these will predominate - usually the most stable one, with least steric crowding (trans > cis). This is exemplified for E1 below;

Unfortunately, the stereochemistry of E2 is more complicated because of the concerted nature of the mechanism.

For most favourable E2, the developing p orbitals on the carbon atoms should be in the same plane as the departing H⁺ and X^-.

This is because the sigma orbital of the C-H bond must feed into the antibonding sigma orbital of the C-X bond, and this is best achieved if they are coplanar. This limits the E2 TS to one of two conformations - anti-periplanar and syn-periplanar, as shown below;

For the following reasons, anti- rather than syn-periplanar elimination is preferred;
1. It allows the greatest separation of the base and the leaving group in the TS.
2. The electrons from the sigma bonding C-H orbital can most easily reach the rear lobe of the C-X sigma antibonding orbital (cf S_N2 where backside attack is favoured for the same reason).
3. It is the most energetically favourable conformer with little torsional strain/ steric crowding.

This has important stereochemical implications if the carbon centres are chiral - syn- and anti- elimination would give different alkene products, and the anti- one should be the major product.

There are some exceptions where syn-periplanar elimination gives the major product - these usually occur when there is some sort of neighbouring group effect, as is shown in the example below;

It is also worth noting that in a cyclic compound undergoing E2, there will not necessarily be a choice between eliminating anti-periplanar or syn-periplanar - if the latter is forced, it will often occur more slowly than it would have done had it been able to anti-eliminate. Also, in cyclohexanes particularly, the most stable conformer may be the one where no trans-diaxial (another way of saying anti-periplanar when referring to cyclic systems) eliminations are possible - in this case (an example is shown below), if the ring cannot achieve a different conformation where trans-diaxial positioning of HX is possible, the rate will be appreciably slower.