Under the Network Function Virtualization multidomain orchestration approach, many service providers jointly manage the lifecycle of network services composed by Virtual Network Functions (VNFs). Many orchestration algorithms have been published focusing on different tasks for the lifecycle of network services. Nowadays, some general-purpose and architectural orchestration surveys have been published. However, currently, no survey classifies and evaluates distributed multidomain orchestration algorithms. In this paper, we focus on multi-domain orchestration works from an algorithm perspective by considering the cooperative and competitive approaches. Algorithms are classified and evaluated. We propose a taxonomy for works that consider different lifecycle tasks of network services. Classification and evaluation are done by identifying key requirements present in competitive and cooperative scenarios. This allows us to have a perspective on the current state of multi-domain orchestration algorithms. We also identify future research directions based on such a current perspective.