SN2 and E2 reactions require a good nucleophile or a strong base. SN1 and E1 reactions occur with strong bases with molecules whose α-carbon is secondary or tertiary and in the absence of good nucleophiles.
This reaction yields SN1 and E1 products: If we disregard ethanol's poor nucleophilicity and weak basicity, this reaction looks very much like an SN2 or E2. The fact that it is not a bimolecular reaction becomes apparent in the SN1/E1 rate law. Remember that the rate law shows which molecules are present in the transition state of the rate- limiting step. Since SN1 and E1 share the same rate law (including k), it is reasonable to assume that both reactions go through the same rate-limiting transition state. That transition state involves a forming carbocation.
Once the carbocation intermediate forms, the two reactions follow divergent pathways. In the SN1 pathway, ethanol acts as a nucleophile. In the E1 pathway, ethanol is a base.
A base/nucleophile as weak as ethanol can substitute or eliminate because the carbocation is an incredibly reactive species. Without the carbocation or a very good leaving group, SN1 and E1 would be impossible.
SN1 and E1 reactions are not synthetically useful because they almost always give a mixture of substitution and elimination products. The proportion of these products does vary with the α-carbon branching, however. Generally speaking, greater branching gives more elimination products. These elimination products generally follow Saytzeff's rule. Keep in mind that the α-carbon must be secondary or tertiary for SN1 or E1 to occur at all. Thus the branching effect is much less pronounced than in the SN2 and E2 reactions.
In the broader context of all substitution and elimination reactions, remember that SN1 and E1 will not occur in the presence of a strong base or a good nucleophile. In these cases, E2 and SN2 dominate their unimolecular cousins.