“The idea of equal access, equal opportunity has sort of evolved in its application from brick and mortar to eCommerce. At first, many companies were worried about the desktop experience. Now, the concern extends to both smart phones and devices.  Wherever a consumer accesses your content – whether it be directly through the web or an app – you need to be concerned about accessibility.”
There have been some notable cases regarding the ADA. For example, two major hotel room marketers (Expedia.com and Hotels.com) with their business presence on the Internet were sued because its customers with disabilities could not reserve hotel rooms, through their websites without substantial extra efforts that persons without disabilities were not required to perform.[58] These represent a major potential expansion of the ADA in that this, and other similar suits (known as "bricks vs. clicks"), seeks to expand the ADA's authority to cyberspace, where entities may not have actual physical facilities that are required to comply.
There have been some notable cases regarding the ADA. For example, two major hotel room marketers (Expedia.com and Hotels.com) with their business presence on the Internet were sued because its customers with disabilities could not reserve hotel rooms, through their websites without substantial extra efforts that persons without disabilities were not required to perform.[58] These represent a major potential expansion of the ADA in that this, and other similar suits (known as "bricks vs. clicks"), seeks to expand the ADA's authority to cyberspace, where entities may not have actual physical facilities that are required to comply.

Until the ADA is updated to address the special case of website accessibility, or the Department of Justice releases its website accessibility regulations, complying with WCAG 2.0 Level AA is the best way to ensure that people with disabilities have equal access to your website. The overview below is a great starting point about meeting the WCAG 2.0 Level AA recommendations.

Because the ADA establishes overlapping responsibilities in both EEOC and DOJ for employment by State and local governments, the Federal enforcement effort is coordinated by EEOC and DOJ to avoid duplication in investigative and enforcement activities. In addition, since some private and governmental employers are already covered by nondiscrimination and affirmative action requirements under the Rehabilitation Act of 1973, EEOC, DOJ, and the Department of Labor similarly coordinate the enforcement effort under the ADA and the Rehabilitation Act.
In an August 2016 case involving the University of California Berkeley, the DOJ ruled that the public university was in violation of ADA Title II (similar to Title III but it instead applies to government organizations) because their YouTube channel’s videos didn’t include captions for hearing impaired visitors. The DOJ found this to violate the ADA as deaf users did not have equal access to the online content.
UPDATE: Since writing this post in August 2017, several important changes have taken place in the laws regarding ADA compliance for websites. On December 26, 2017, the Department of Justice announced that they have withdrawn the Obama-era Advance Notice of Proposed Rulemaking mentioned in this article which intended to require ADA website compliance. The DOJ’s withdrawal announcement stated, “The Department will continue to assess whether specific technical standards are necessary and appropriate to assist covered entities with complying with the ADA.”
Most recently, however, pizza chain Domino's has been brought under suit for their website not being accessible for specialty ordering. The U.S. Supreme Court refused to review the case, instead upholding the decision of the 9th U.S. Circuit Court of Appeals who said the “alleged inaccessibility of Domino’s website and app impedes access to the goods and services of its physical pizza franchises—which are places of public accommodation.”
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