With the rapid growth of schemes and initiatives to promote e-mobility and numerous measures taken to ensure its quick and effective implementation, there is a wide range of technological and non-technological problems, especially organisational, economic, legal and social in nature, that have to be handled by national and local governments all over the world. This article addresses some of the technological and organisational challenges for electromobility. The key technology-related issues to be coped with are the need for longer ranges of electric vehicles (EVs), shorter charging times and smart power grids (because of a higher demand for electrical energy). Another important problem to be solved urgently is the high battery weight, affecting the vehicle dynamics. Because of the excessive weight of the battery pack, there is a risk of its displacement during a crash, which may jeopardize the safety on the road. The next big concern, also associated with safety, is protection against electrical and fire hazards in the event of a collision. The most important of all the organisational challenges related to EVs is the necessity to create networks of charging stations. Their insufficient number and unsatisfactory distribution are strong barriers hampering the development of e-mobility. The organisational measures also include privileges such as access to bus lanes, already offered in some countries. Finally, there is the need to urgently train a large number of electricians to test and maintain EVs, the need to create a recycling system for used EV batteries, and the need to deal with the organisational aspects of the development of smart power grids.