Bibliometrics refers to the quantitative study of scholarly literature, mainly through the analysis of citations to authors' works and to journals. The metrics calculated from citation counts are used to determine the impact of an author or journal in a discipline. Examples of bibliometrics are citations counts for individual scholarly works,  h-indices for authors and journals, and the Journal Impact Factor. Commonly used resources that provide bibliometrics are:

• Web of Science - author metrics
• Scopus - author and journal metrics
• Journal Citation Reports - journal metrics
• Google Scholar - author and journal metrics

In the past 10 years, bibliometrics have come under criticism for the following reasons: 

• social sciences and especially the humanities are underrepresented in databases that provide bibliometrics
• the metrics are a poor measure of impact in disciplines where little citing is done, e.g., the humanities
• it takes 3-4 years to generate bibliometrics from time of publication because of their dependence on citations
• the metrics are being used improperly as the main evaluation tool for promotion and tenure

Learn more about bibliometrics from these sources:

• Beyond Bibliometrics: Harnessing Multidimensional Indicators of Scholarly Impact, edited by Cronin and Sugimoto, Discovery Park Library
• San Francisco DSycamore Libraryaration on Research Assessment
• Metrics Toolkit, a rich resource containing definitions of metric and altmetrics that apply to authors, articles, journals, books and more. Filter by product type, type of impact, or discipline to find the best scholarly metrics for your work. The editorial board consists of librarians and a director at Altmetric.

Altmetrics is the quantitative study of communications about scholarly works from measures other than citations. These measures may include article views and downloads, inclusion in citation managers,  references in social media such as Facebook, Twitter and/or blogs, Wikipedia, and the popular press. Numbers of communications indicate the impact of a scholarly work in a discipline. The benefits of altmetrics are 1) the ability to show the impact of a work earlier than the point of citation, and 2) to show activity in disciplines where less citation is done. Currently, altmetrics are not widely accepted as evidence of impact by university promotion and tenure committees, but there are indications that the monopoly of bibilometrics is breaking down. See these links for more details about altmetrics.

• Altmetrics: A Manifesto, 2010 from Altmetrics.org
• Altmetrics: A Practical Guide for Librarians, Researchers and Academics, edited by Tattersall, an online book at UNT Libraries
• The Altmetrics Collection, a collection of research articles and essays about altmetrics from the Public Library of Science
• Altmetric, an almetrics provider
• Metrics Toolkit, a rich resource containing definitions of metric and altmetrics that apply to authors, articles, journals, books and more. Filter by product type, type of impact, or discipline to find the best scholarly metrics for your work. The editorial board consists of librarians and a director at Altmetric.

The HumMetricsHSS initiative is "rethinking humane indicators of excellence in the humanities and social sciences" in response to the over-dependence on bibliometrics to evaluate scholars in higher education. It is a value-based approach to measure a scholar's progress based on five core values central to the humanities and social sciences: 

1. COLLEGIALITY, which can be described as the professional practices of kindness, generosity, and empathy toward other scholars and oneself.
2. QUALITY, a value that demonstrates one’s originality, willingness to push boundaries, methodological soundness, and the advancement of knowledge both within one’s own discipline and among other disciplines and with the general public, as well.
3. EQUITY, or the willingness to undertake study with social justice, equitable access to research, and the public good in mind.
4. OPENNESS, which includes a researcher’s transparency, candor, and accountability, in addition to the practice of making one’s research OPEN ACCESS at all stages.
5. COMMUNITY, the value of being engaged in one’s community of practice and with the public at large and also in practicing principled leadership.

An October 2017 blog explains the origin of the initiative.