One of the main objectives of this paper is to address the following question: When is the global CR automorphism group of a CR manifold a Lie group in an appropriate topology? We give here sufficient geometric conditions on a CR manifold $M$ to guarantee that the group of all its smooth (and real-analytic when $M$ is real-analytic) CR automorphisms has the structure of a (finite-dimensional) Lie group compatible with its natural topology.