The SN2 and E2 mechanisms require a good nucleophile or a strong base. In contrast, SN1 and E1 mechanisms need weak nucleophiles and bases.
The nucleophiles and bases in SN1 and E1 reactions aren't strong enough to eject the leaving group by themselves. Instead, both SN1 and E1 reactions are characterized by the formation of a common carbocation intermediate. Even weak bases and poor nucleophiles will react with the carbocation.
The carbocation intermediate lends a number of unique features to SN1 and E1 reactions. First, both mechanisms require a stable carbocation intermediate. Thus SN1 and E1 will only work for secondary or tertiary α-carbons**. Second, SN1 and E1 reactions involve a carbocation intermediate and are not concerted. Because of the geometry of the carbocation and their non- concerted nature, both reactions result in a loss of stereochemical configuration. Third, SN1 and E1 reactions are favored by polar, protic solvents. Polar, protic solvents stabilize the carbocation. Fourth, secondary carbocations may rearrange to form tertiary carbocations. This greatly increases the number of products.