We study mobile systems, i.e. systems with a dynamically changing communication topology, from a process algebras point of view. Mobility can be introduced in process algebras by allowing names or terms to be transmitted. We distinguish these two approaches as first-order and higher-order. The major target of the thesis is the comparison between them. The prototypical calculus in the first-order paradigm is the π-calculus. By generalising its sort discipline we derive an w-order extension called Higher-Order π-calculus (HOπ). We show that such an extension does not add expressiveness to the π-calculus: Higher-order processes can be faithfully compiled down to first-order, and respecting the behavioural equivalence we adopted in the calculi. Such an equivalence is based on the notion of bisimulation, a fundamental concept of process algebras. Unfortunately, the standard definition of bisimulation is unsatisfactory in a higher-order calculus because it is over-discriminating. To overcome the problem, we propose barbed bisimulation. Its advantage is that it can be defined uniformly in different calculi because it only requires that the calculus possesses an interaction or reduction relation. As a test for barbed bisimulation, we show that in CCS and π-calculus, it allows us to recover the familiar bisimulation-based equivalences. We also give simpler characterisations of the equivalences utilised in HOπ. For this we exploit a special kind of agents called triggers, with which it is possible to reason fairly efficiently in a higher-order calculus notwithstanding the complexity of its transitions. Finally, we use the compilation from HOπ to π-calculus to investigate Milner's