In the talk we review the results about retrial queues and networks with constant retrial rate. Speci fically we consider a network of queues with finite waiting room capacities. Jobs travel through the network by paths given by some routing matrix. If a job fi nds a queue with no available waiting space it goes into the orbit queue corresponding to the job's path. At the orbit the jobs wait for retrial in the first-come, first-served fashion. Thus, the rate of retrial does not depend on the number of jobs in the orbit. Computer networks with mice-type TCP traffic and ALOHA-type access protocols are examples of the applications for the proposed model. The problem appears to be very challenging for analysis. We provide some analytical results for the case of one node. In particular, we provide stability conditions with clear probabilistic interpretation. For the case of network we suggest approximations based on mean value and fi xed point approaches. We also discuss optimization problems for one node and network.