In this book, a detailed review of the recent developments and applications in the areas of queue with catastrophes, feedback, vacations and breakdowns are presented. Chapter 2 illustrates how generating function technique can be used to obtain the transient solution of a nonempty M/M/1 queueing system subject to catastrophes, server failures and repairs. Chapter 3 analyses an M/M/1 queueing system with instantaneous Bernoulli feedback subject to catastrophes, server failures and repairs. Continued fraction methodology has been employed to obtain a transient solution for the system size probabilities in closed forms. Chapter 4 concerns with an M/G/1 Bernoulli feedback queueing system providing two types of service with optional single vacations and random breakdowns. Chapter 5 deals with a batch arrival Bernoulli feedback queueing system in which the server provides two phases of heterogeneous service with compulsory vacations and random breakdowns. In both the chapters, the transient state probabilities of system size in terms of their Laplace transforms are derived using the supplementary variable technique.