Mobile phones are becoming increasingly important in monitoring and delivery of healthcare interventions. They are often considered as pocket computers, due to their advanced computing features, enhanced preferences and diverse capabilities. Their sophisticated sensors and complex software applications make the mobile healthcare (m-health) based applications more feasible and innovative. In a number of scenarios user-friendliness, convenience and effectiveness of these systems have been acknowledged by both patients as well as healthcare providers. M-health technology employs advanced concepts and techniques from multidisciplinary fields of electrical engineering, computer science, biomedical engineering and medicine which benefit the innovations of these fields towards healthcare systems. This paper deals with two important aspects of current mobile phone based sensor applications in healthcare. Firstly, critical review of advanced applications such as; vital sign monitoring, blood glucose monitoring and in-built camera based smartphone sensor applications. Secondly, investigating challenges and critical issues related to the use of smartphones in healthcare including; reliability, efficiency, mobile phone platform variability, cost effectiveness, energy usage, user interface, quality of medical data, and security and privacy. It was found that the mobile based applications have been widely developed in recent years with fast growing deployment by healthcare professionals and patients. However, despite the advantages of smartphones in patient monitoring, education, and management there are some critical issues and challenges related to security and privacy of data, acceptability, reliability and cost that need to be addressed.