Abstract: The paper discusses space tethers of two principal categories: the momentum exchange tether and the electro-dynamic tether. Fundamental theory, dynamic models and control strategies, as well as space tether technology and mission development, practical tether designs and survivability are included in the discussion. It is shown that that dynamics and control are the two fundamentally important aspects of all tether concepts, designs, and mission architectures. Some interesting topics and the developing directions of space tether in future are suggested.