It can also include regulation of density. Zoning also controls uses within districts. There are a number of devices to provide flexibility in the zoning ordinance. Many ordinances allow their continuation unless they are destroyed or damaged to a certain percentage. Some ordinances require that non-conforming structures be amortized and discontinued after a certain period of time.
Amendments are changes in the ordinance.
The major issue here is to avoid the problem of spot zoning. Note that one can rezone a single parcel and this is not necessarily illegal. In addition, variance requirements usually mandate a finding that the hardship was not brought on by the applicant, and that the proposed use will not be at variance with the zoning scheme of the character of the neighborhood. The individual provisions may vary from place to place. Personal hardship is not supposed to be grounds for granting a variance.