The growth of the Internet and its acceptance has sparkled keen interest in the research community in respect to many apparent scaling problems for a large infrastructure based on IP technology. A self-contained problem of considerable practical and theoretical interest is the longest-prefix lookup operation, perceived as one of the decisive bottlenecks. Several novel approaches have been proposed to speed up this operation that promise to scale forwarding technology into gigabit speeds. This paper surveys these new lookup algorithms and classifies them based on applied techniques, accompanied by a set of practical requirements that are critical to the design of high-speed routing devices. We also propose several new algorithms to provide lookup capability at gigabit speeds. In particular, we show the theoretical limitations of routing table size and show that one of our new algorithms is almost optimal, while requiring only a small number of memory accesses to perform each address lookup.