Trademark law protects distinctive words, phrases, logos, symbols, slogans, and any other devices used to identify and distinguish products or services in the marketplace. Trademarks are often registered with the U.S. Patent & Trademark Office, creating a nationwide system of protection.
Trademark infringement is the unauthorized use of another person or company's registered trademark. For example, if you wanted to start making electronic gadgets and decided to stamp Apple's recognizable fruit-shaped logo onto your products, this would be fairly obvious trademark infringement. Customers are likely to be confused about the origin of the goods, and you would essentially be profiting off of the goodwill that Apple has generated over many decades.
But are there any circumstances under which you would be permitted to use a trademark without the prior permission of its owner? The short answer is that you can use a trademark belonging to another person or company if you use the mark for:
Informational (or “editorial”) uses of a trademark do not require permission. These are uses that inform, educate, or express opinions protected under the First Amendment of the United States Constitution—freedom of speech and of the press.
For example, permission is not required to use the Chevrolet logo in an article describing Chevrolet trucks, even if the article is critical of the company. You could (obviously) use the word mark "Chevrolet" as well as the famous golden "plus sign" logo mark. This would be true whether you were publishing a news article or an article in an academic journal.
Similarly, if you were making a documentary film on the history of American trucks, you would not need permission to include the Chevrolet logo. However, the use of the logo must have some relevance to the work. For example, it would not be wise to publish an article critical of overseas auto manufacturing practices and include the Chevrolet logo unless Chevrolet was mentioned in the article.
Finally, you are also permitted to use trademarks for purposes of parody or commentary. For example, if you were writing a skit about how young people are always on their phones, you could glue the Apple logo onto the actors' prop phones without fearing a claim of trademark infringement.
Under trademark law, you are generally permitted to use a trademark as a means for comparison. For example, you could create a newspaper advertisement that incorporates your mark and your competitors' marks in order to describe a difference between the companies. Imagine that you make a type of coffee that you believe to be tastier and less expensive than any other company's product. You could include on your advertisement the logo of Starbucks along with the price of its comparable drink.
Two important caveats here, however. First, you may not alter your competitors' trademarks in a way that is derogatory or misleading. (For example, you cannot dress up as Ronald McDonald and make him look unattractive!). These activities could make you subject to a claim of trademark disparagement.
Second, any comparative information that you use must be accurate. While subjective statements (what tastes better, what's easier to use, and so forth) are hard to judge for accuracy, factual information is not. So if you say that Starbucks charges $3.50 for a 12-ounce black coffee, that fact needs to be demonstrably true. If you say that Apple uses deadly chemicals in its iPhones that could leak into users' hands, that also would need to be true. In other words, any lies associated with your use of a competitor's trademark could open you up to a claim of trademark infringement or disparagement.