Abstract: The numbers in question are the convergent sums \zeta(k_1, \dots, k_n) = \sum_{0 < m_1 < \dots < m_n} \frac{1}{m_1^{k_1} \cdots m_n^{k_n}}where the k_i are positive integers with k_n at least equal to 2. Thesenumbers, first studied by Euler, have come up in recent years in a surprisingly wide variety of contexts, including knot invariants and calculations of Feynman integrals in perturbative quantum field theory. Their study requires a mixture of elementary and abstract techniques, and leads to many nice identities. A survey of some recent developments, and of a "mod p" analogue, will be given.