Current workflow management systems need a deep insight into the design of organization’s business process. Creating a business workflow design is sometimes complicated, inaccurate, time-consuming and non-error free. This business process design requires adequate tools and techniques needed to help organizations or companies achieve their desirable target. To aid the support of workflow, scholars have proposed the use of workflow mining which helps organizations have a deep insight into their business processes. This study gives an in-depth analysis on the current trend of workflow mining and also discusses their strengths and limitations/weaknesses. Most existing approaches produces models that are generalized, incomplete, not well represented and shows only fuzzy pictures of the workflow investigated. The challenging issues that arise as a result of inaccurately applying the right algorithm to construct a work model from workflow logs are also highlighted. There is need to make appropriate selection for a good mining algorithm to avoid any setback and understanding the organization business workflow processes for business design, modeling, resource strategy and planning control. It is essential to have a comprehensive characterization study of workflow mining algorithms. The resulting insights provides a foundation for such workflow mining algorithms necessary for improving business processes schemes as well as for the effectiveness of future services and application