Parallelizing logic programming has attracted much interest in the research community, because of the intrinsic or and and parallelisms of logic programs. One research stream aims at transparent exploitation of parallelism in existing logic programming languages such as Prolog while the family of concurrent logic languages develops constructs allowing programmers to express the concurrency, that is the communication and synchronization between parallel process, inside their algorithms. This paper mainly concentrates on transparent exploitation of parallelism and surveys the most mature solutions to the problems to be solved in order to obtain efficient implementations. These solutions have been implemented and the most efficient parallel logic programming systems reach effective speedups over state-of-the-art sequential Prolog implementations. The paper also addresses current and prospective research issues aiming to extend the applicability and the efficiency of existing systems,such as models merging the transparent parallelism and the concurrent logic languages approaches, combination of constraint logic programming with parallelism and use of highly parallel architectures.