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George Siemens and Stephen Downes developed a theory for the digital age, called connectivism, denouncing boundaries of behaviorism, cognitivism, and constructivism. Connectivism is the thesis that knowledge is distributed across a network of connections, and therefore that learning consists of the ability to construct and traverse those networks. An account of connectivism is therefore necessarily preceded by an account of networks. Current developments with technology and social software are significantly altering: (a) how learners access information and knowledge, and (b) how learners dialogue with the instructor and each other. Both of these domains (access and interaction) have previously been largely under the control of the teacher or instructor. Since half of what is known today was not known 10 years ago, there should be more researches about the use, benefits and drawbacks of connectivism in the cotext of formal and informal lerning. Although there is not a large amount of research currently available on the application of connectivism in education, some possible applications, such as: social networking, personal learning environments and open courseware are explained.