The distribution theory of runs and patterns has becoming increasingly useful in applied statistics and in biomedical research in particular, with numerous applications to, for example, health care evaluation and computational biology. Statistical challenges associated with the problem-specific statistics involving runs and patterns often arise from non-iid assumptions in practical settings. The aim of this talk is to present how such challenges can be addressed using the method of finite Markov chain imbedding (FMCI). A brief overview of the FMCI approach will be given, and the focus of the discussion will be its usage in some selected practical applications, including HIV patient care and DNA sequence homology.