In the introductory chapter of this book, a detailed review on the recent developments and applications in the areas of retrial queue with two phases of service, feedback, vacations and breakdowns are presented.Chapter 2 analyses an M/G/1 retrial queueing system with two phases of service and the server is subject to breakdown while servicing at any of the phases of service. Chapter 3 concerns with a batch arrival retrial queue with two phases of service, feedback and K-optional vacations. Supplementary variable method has been employed to obtain the steady state solution for system size probabilities. In both the chapters, steady state analysis of system size probabilities, stability condition and some performance measures of the systems are deduced.Chapter 4 deals with a batch arrival retrial queueing system in which the server provides two phases of heterogeneous service with feedback, k-optional vacations and random breakdowns. System performance measures and particular cases of interest of this model have been discussed. Finally, numerical illustrations are provided to reveal the operational effect of parameters on system performance measures.