This article describes queueing systems and queueing networks which are successfully used for performance analysis of different systems such as computer, communications, transportation networks and manufacturing. It incorporates classical Markovian systems with exponential service times and a Poisson arrival process, and queueing systems with individual service. Oscillating queueing systems and queueing systems with Cox and Weibull service time distribution as examples of non-Markovian systems are studied. Jackson's, Kelly's and BCMP networks are also briefly characterized. The model of Fork-Join systems applied to parallel processing analysis and the FES approximation making possible of Fork-Join analysis is also presented. Various types of blocking representing the systems with limited resources are briefly described. In addition, examples of queueing theory applications are given. The application of closed BCMP networks in the health care area and performance evaluation of the information system is presented. In recent years the application of queueing systems and queueing networks to modelling of human performance arouses researchers' interest. Hence, in this paper an architecture called the Queueing Network-Model Human Processor is presented.