Background:The reconstruction of clonal haplotypes and their evolutionary history in evolving populations is a common problem in both microbial evolutionary biology and cancer biology.The clonal theory of evolution provides a theoretical framework for modeling the evolution of clones.Results:In this paper,we review the theoretical framework a nd assumptions over which the clonal reconstruction problem is formulated.We formally define the problem and then discuss the complexity and solution space of the problem.Various methods have been proposed to find the phylogeny that best explains the observed data.We categorize these methods based on the type of input data that they use (space-resolved or time-resolved),and also based on their computational formulation as either combinatorial or probabilistic.It is crucial to understand the different types of input data because each provides essential but distinct information for drastically reducing the solution space of the clonal reconstruction problem.Complementary information provided by single cell sequencing or from whole genome sequencing of randomly isolated clones can also improve the accuracy of clonal reconstruction.We briefly review the existing algorithms and their relationships.Finally we summarize the tools that are developed for either directly solving the clonal reconstruction problem or a related computational problem.Conclusions:In this review,we discuss the various formulations of the problem of inferring the clonal evolutionary history from allele frequeny data,review existing algorithms and catergorize them according to their problem formulation and solution approaches.We note that most of the available clonal inference algorithms were developed for elucidating tumor evolution whereas clonal reconstruction for unicellular genomes are less addressed.We conclude the review by discussing more open problems such as the lack of benchmark datasets and comparison of performance between available tools.