This article defines 27 criteria for evaluating the functionality of e-learning platforms, grouped into three macro groups: (a) learning management, (b) learning content management, and (c) communications and collaboration tools. The proposed criteria can be used to evaluate any e-learning platform's functionality. They allow teachers and administrators to make conscious choices about the highest-quality e-learning platform for their schools and developers to improve e-learning platforms' functionality. The developed criteria became the basis for rating the functionality of Ukrainian developers' eight e-learning platforms' and determining the degree of support (in whole or partly) of e-learning components, categorized on the cognitive, social constructivist, motivation, and e-learning theories (CT, SCT, MT, and E-LT). The results indicate that the lack of communication and collaboration tools necessary to ensure quality distance learning is the main problem of Ukrainian e-learning platforms. Comparative analysis of the functionality of e-learning platforms and components categorized on the learning theories helped determine that only three of the eight Ukrainian e-learning platforms (Accent [Mobischool], Class Assessment, My Class) fully follow the CT, SCT, and MT, but these platforms are all commercial products; therefore, they only partially support the E-LT. Solving this problem will be facilitated by developing e-learning platforms with open access, financed by the state budget in the context of the development of open and distance learning for Ukrainian students, as well as improving communication and collaboration tools in the context of conforming e-learning components to the social constructivist learning theory.