An author's h-index, or Hirsch index, is the number (integer) n for which the author has published at least n papers which have each been cited at least n times. Eg
Impact factors attempt to measure the importance of a journal based on how often its articles are cited in the field.
Obvious factors can heavily influence journal impact factors, such as journal title changes, or publishers gaming the system by requiring authors to cite articles from other journals by the same publisher. However there are more systematic problems:
Symplectic Elements - as well as standard metrics such as SNIP and SJR, Elements provides Altmetrics e.g. number of times an output has picked up by news outlets, tweets, blogs, Mendeley, CiteULike, Facebook etc
Ebsco databases (e.g PsycInfo, Business Source Complete) now include PlumAnalytics
Web of Science provides download statistics for articles
Some journal web-sites also provide altmetric statistics