Astronomy and Cosmology are science disciplines that give an in-depth description and analysis of the structures and forms that characterize the universe. Although Astronomy and Cosmology are not yet fully developed in the East African region, several affirmative developments have been registered in the establishment of the disciplines in the region. These include, among others: postgraduate training of students from Uganda, Kenya, Rwanda and Ethiopia in South Africa since 2003, benefiting from the South African National Astrophysics and Space Science Programme (NASSP) and the Square Kilometre Array (SKA) Project. Some of these have since graduated with PhDs and returned to their home countries to contribute to the development of the disciplines. The Entoto Observatory in Ethiopia has been commissioned to provide infrastructure for Observational Astronomy and outreach activities. Kenya will host some Radio Astronomy telescopes under SKA. Most public universities in Ethiopia offer Astronomy at undergraduate level, while a few offer it at postgraduate level. In Kenya, Astronomy has been introduced at undergraduate level at the University of Nairobi and Kenyatta University, respectively. In Uganda, Mbarara University of Science and Technology leads by offering Astronomy as major components of Physics at both undergraduate and postgraduate levels, and many graduate students do projects/research in Astrophysics. In Rwanda, the National University of Rwanda also offers Astronomy as a component of Physics for undergraduate students. Since 2009, the East African Astronomical Society (EAAS) has been formed and workshops have been held in Kenya, Ethiopia, Uganda and Rwanda, respectively. In 2013, the East African Astronomical Research Network (EAARN) was formed by astrophysicists, with the sole aim of improving research capacity and collaboration in Astrophysics. Although Makerere University is the oldest public university in Uganda and among the top ranking universities in Africa, Astronomy is yet to be fully developed. An effort has been made to introduce it as taught components of Physics at undergraduate and postgraduate levels. This has created awareness among students and also cultivated much interest in pursuing further careers in Astrophysics. The university has at least employed on full-time one professional Astrophysicist who may spearhead the establishment of the field. Initially, part-time lecturers were being engaged to help teach astronomy related courses. Successful establishment of Astronomy at Makerere University will require adequate resources, which are lacking at the moment. However, with support, collaborations and graduate training, this can be achieved.