Diplomas are the physical manifestation of your degrees. They typically bear your name, the degree you received, the Columbia Seal, and the signatures of the university president and the dean of your school. Diplomas are mailed to you after Commencement.
Columbia uses a single English-language diploma design for all of its schools and degree programs with a limited number of exceptions. Specifically, (1) diplomas for Columbia College are nearly identical to standard design, except the writing is in latin; (2) diplomas for Columbia Law School mirror the standard design except they are in latin, similar to Columbia College, and physically larger in size; (3) the College of Physicians and Surgeons diploma bears little resemblance to the shared design language of all other Columbia diplomas.
In addition, the Trustees of Columbia University also confer degrees on graduates of Barnard College, who receive a latin language diploma similar to those granted to Columbia College graduates, but including both the Columbia University and Barnard College seals.
Columbia's standard diploma size (10.5" by 12.5") isn't actually standard at all, which means you have to pay for the overpriced frames sold in the bookstore or get a frame custom made. A (relatively) cost-effective alternative is to use a 'floating' frame design, which may give you options among standard size off-the-shelf frames.
If your diploma gets damaged or lost and you want to get it replaced, you need to send $100 along with a notarized application to the Registrar.  While the new diploma will display your date of graduation, it will bear the signatures of the current university president and dean of your school, who may be different from when you graduated.
The current standard diploma design dates back to the early 1900s. The one exception to the standard design was the Columbia College diploma, which was uniquely printed in latin. The design went largely unchanged, except for slight changes in typography, until approximately 2007.
In the 1980s, the College of Physicians and Surgeons redesigned their diplomas entirely. Shortly thereafter, the Law School also redesigned its diplomas. Unlike the medical school, the Law School decided to maintain the general design of the standard diploma, but borrowed (most) of the latin inscription from Columbia College, and blew up the diploma in size.
In 2003-2004, GS student and University Senator Matan Ariel spearheaded an effort to redesign Columbia's diplomas as part of the C250 celebrations, hosting an online poll and passing a University Senate resolution urging the Trustees to look into the issue. Ariel and the Diploma Task-Force of fellow students consulted with a representative from the Registrar and the Jostens company to generate four new designs.
Although there is no record of an official change, the the standard diploma design changed by 2007 in ways responsive to complaints highlighted by Ariel's task force, namely by altering the typography to place greater emphasis on the school name, the student's name, and the degree earned on the diploma. Most noticeably, the layout was reformatted so that for the first time "The Trustees of" and "Columbia University" appeared on two lines, with the latter in a much larger font. In addition, the University Seal, which had been located on the lower left corner of the diploma, while the signatures of the University President and School Dean were located the lower right corner, was moved to the center of the bottom, while the signatures were split up and moved to the two lower corners.
GS students, who had responded to Ariel's initiative by asking for the latinization of their english-language diplomas, raised the issue again in 2009-2010. However, Dean Peter Awn quashed the idea, stating that a latin diploma was inappropriate for a school founded in 1947 with a non-traditional mission. Awn also cited that it seemed like an inappropriate allocation of resources to make the necessary logistical changes in a time of fiscal restraint. Awn also found it "difficult to grasp why any student would want a diploma written in a language that he or she could not understand."
- As it turns out, getting the registrar to provide an actual description of the diploma, e.g. the weight, quality, and material of the paper, etc. is impossible. They cite security reasons. I guess they think someone will try to forge a copy if they let that information out. It's not like they practically hand these things out.
- Curiously, the latin translation provided with the diplomas suggests that the English language diplomas are not exact translations of the latin ones (or vice versa, if you prefer).
- Law School diplomas followed the standard format until a redesign sometime in the 1980s, according to the website for University Senator Matan Ariel's 2004 Diploma Redesign Initiative. According to that website, the law school redesign followed on the heels of a complete redesign of the M.D. diploma
- According to the website for University Senator Matan Ariel's 2004 Diploma Redesign Initiative, the CPS diplomas were redesigned "about 20 years ago." Prior to that they were issued in the standard design.
- The conferral of degrees on Barnard graduates by Columbia University is a legacy of the close relationship between the the two institutions dating back to Barnard's founding at the turn of the 20th century, and is formally ratified as part of the Columbia-Barnard Intercorporate Agreement.
- "[T]he standard diploma was designed roughly 100 years ago and has not been changed since." Columbia University Senate Student Affairs Caucus Diploma Design Poll (2004). This would make the Columbia diploma design yet another legacy of the Nicholas Murray Butler university presidency.
- "[A]bout 20 years ago the medical school changed its diplomas to a very different design from the standard diploma." Columbia University Senate Student Affairs Caucus Diploma Design Poll (2004).
- "[S]hortly after the medical school changed its diploma, the law school redesigned its diplomas as well." Columbia University Senate Student Affairs Caucus Diploma Design Poll (2004)
- E-mail feedback received by Ariel and the Task-Force was anonymized and collected in a report presented to the administration.
- Exemplars of the four proposed designs can be found in the University Archives.
- Regarding the School of General Studies Diploma (E-mail from Dean Peter Awn to Students) March 10, 2010