Owing to a large number of applications periodic pattern mining has been extensively studied for over a decade. Periodic pattern is a pattern that repeats itself with a specific period in a give sequence. Periodic patterns can be mined from datasets like biological sequences, continuous and discrete time series data, spatiotemporal data and social networks. Periodic patterns are classified based on different criteria. Periodic patterns are categorized as frequent periodic patterns and statistically significant patterns based on the frequency of occurrence. Frequent periodic patterns are in turn classified as perfect and imperfect periodic patterns, full and partial periodic patterns, synchronous and asynchronous periodic patterns, dense periodic patterns, approximate periodic patterns. This paper presents a survey of the state of art research on periodic pattern mining algorithms and their application areas. A discussion of merits and demerits of these algorithms was given. The paper also presents a brief overview of algorithms that can be applied for specific types of datasets like spatiotemporal data and social networks.