Lattice reduction algorithms have surprisingly many applications in mathematics and computer science, notably in cryptology. On the one hand, lattice reduction algorithms are widely used in public-key cryptanalysis, for instance to attack special settings of RSA and DSA/ECDSA. On the other hand, there are more and more cryptographic schemes whose security require that certain lattice problems are hard. In this talk, we survey lattice reduction algorithms, present their performances, and discuss the differences between theory and practice.