Network motif is defined as a frequent and unique subgraph pattern in a network, and the search involves counting all the possible instances or listing all patterns, testing isomorphism known as NP-hard and large amounts of repeated processes for statistical evaluation. Although many efficient algorithms have been introduced, exhaustive search methods are still infeasible and feasible approximation methods are yet implausible. Additionally, the fast and continual growth of biological networks makes the problem more challenging. As a consequence, parallel algorithms have been developed and distributed computing has been tested in the cloud computing environment as well. In this paper, we survey current algorithms for network motif detection and existing software tools. Then, we show that some methods have been utilized for parallel network motif search algorithms with static or dynamic load balancing techniques. With the advent of cloud computing services, network motif search has been implemented with MapReduce in Hadoop Distributed File System (HDFS), and with Storm, but without statistical testing. In this paper, we survey network motif search algorithms in general, including existing parallel methods as well as cloud computing based search, and show the promising potentials for the cloud computing based motif search methods.