Rhetoric can be both discursive and non discursive, usually dealing with persuasion and argument. Discursive rhetoric is EXPLAIN. Non-discursive rhetoric is EXPLAIN.
Rhetoric may refer to discourse—spoken or written, usually dealing with persuasion and argument. Rhetoric may also be non-discursive in terms of visuals. (ask Derek more about non-discursive rhetoric... ) In modern rhetoric, the concepts have become more foundational, and not simply applied to persuasive techniques in miscommunication. In practice with student writers this underlines that writing, communication, and inventional work is participating in a community--it is being aware of audiences and purposes all the time. Rhetoric is how we know, and how we connect and relate, not reserved for only when we "trick" others. Furthermore in considering how we communicate with others, we are caring for our relationships in regard to ethics, even if we are not explicitly discussing ethics.
Susan Harkness Regli. The Technical Writer's Expertise in Inventio. SHR has a great discussion of understanding rhetoric less eristically, and more as invention, and how invention is developing knowledge communication.
Carolyn Miller. "What's Practical about Technical Writing?"
In defense of rhetoric: not just for liars video -- rhetorical situations page on the Purdue OWL
The art of Rhetoric traces back to ancient Greece but can more recently be linked to the 19th century philosopher, Aristotle, who defines Rhetoric as "the faculty of observing in any given case the available means of persuasion.” In discussing these means of persuasion, Aristotle identifies 3 ways to appeal to an audience: Ethos, Pathos, and Logos.
Ethos: ethical appeals based on character, credibility, and reliability. In rhetoric, ethos are used as a mode of persuasion, and a rhetor’s ethos needs to be established from the start. For example, if a mayoral candidate is trying to convince the public that he/she is credible and should be re-elected, they will try to establish their ethos by saying what positive contributions they have made to the community, how they support the education of children, and why they are qualified for the position.
Pathos: appeals to an audience’s needs, values, and emotional sensibilities. Similar to ethos, in rhetoric, pathos is also a mode of persuasion, but this mode focuses particularly on appealing to an audience through emotion so as to “induce them to make the judgment desired.” For example, to convince us the dangers of second-hand smoke, an advertising company might show pictures of sickly children coughing in a dark room surrounded by smoke in order to make us feel guilty or bad for making children suffer.
Logos: appeal to reason that relies on logic or reason. Often depends on the use of inductive or reductive reasoning “Originally logos referred to the actual content of the speech and how it was organized.” 
There are, however, instances where ethos, pathos, and logos may not cover the appeals someone may make toward an audience. In this instance, "nomos" and "mythos" may be considered as appendages:
Nomos: appeals to law/rule. Say more.
Mythos: appeals to doxa/myth. Say more.
Though not introduced by Aristotle, Kairos can also be discussed when explaining how rhetoric functions.
Why is it useful?
The study of Rhetoric can be useful in a number of contexts. In order to be successful in a multitude of communication contexts (ranging from everyday conversations to situations where you need to convince someone of your position) understanding the kind of language to use it is necessary to understand the rhetorical situation.
Where can Rhetoric be found in the world?
Because Rhetoric can be both discursive and non-discursive, it can be found in almost any communication context. Say more.
Where can Rhetoric be found in Academics?
The study of Rhetoric is typically housed in either English and Communication Departments, depending on the type of discourse they study.
Within the field of Rhetoric there are several concentrations including, but not limited to:
Contemporary Rhetorical Theory
Writing Center Studies
Rhetoric of Science
Technological Rhetoric/Rhetoric of Technology
This is great, but where can I learn more about Rhetoric?
Place links here where people can learn more
- Tancred, Hughes-Lawson, and Aristotle. The Art of Rhetoric. London: Penguin, 1991. Print.
- Kennedy, George, and Aristotle. "Aristotle on Rhetoric: A Theory of Public Discourse." Journal of Advanced Composition. 13.1 (1993): 273-276. Print
- Definitions adopted from Purdue Owl Writing Lab http://owl.english.purdue.edu/owl/resource/588/04/