The Teyjus system is an efficient implementation of the higher-order logic programming language Lambda Prolog. The main strength of Lambda Prolog, a language developed by Dale Miller and Gopalan Nadathur, is the support it offers for what is known as lambda tree syntax, a new and effective way to view the structure of complex syntactic objects such as types, formulas, proofs and programs. Lambda Prolog provides this support by using lambda terms as data representation devices and by including primitives for probing such terms in logically meaningful ways. The new features present in the language raise several implementation challenges that have been addressed in collaborative work between Nadathur and his students and colleagues. The name "Teyjus" actually stands both for a project and for a class of compiler and virtual machine based realizations of Lambda Prolog arising from the research carried out within this project. Underlying the most recent version of the Teyjus system is a new and significantly improved virtual machine that has been designed by Xiaochu Qi as part of her doctoral dissertation work at the University of Minnesota. This virtual machine extensively exploits a special form of higher-order unification known as pattern unification.