This paper firstly describes the research framework of Human Activity Recognition and Fall Detection, as well as Hidden Markov Model and its extension with continuous observations and hierarchical topology, namely the Continuous Density Hidden Markov Model and the Hierarchical Hidden Markov Model. Subsequently, we introduce how to apply Hidden Markov Models to the human activity modeling in Human Activity Recognition and Fall Detection based on previous literature. Finally, famous research work for smart home technology and elderly care based on Hidden Markov Models is reviewed.