Contrary to the long-held belief that phase transitions occur only in the thermodynamic limit of infinite number of constituents, it has been recently found that finite-component systems of coupled spins and bosons may exhibit all the hallmarks of the quantum phase transition in a closed system and the dissipative phase transition in an open quantum system . In this talk, I will introduce the notion of finite-component system phase transitions in both closed and open quantum systems and show how the simultaneously large spin-boson coupling strength and detuning lead to the thermodynamic limit of infinite excitations. I will focus on a few paradigmatic models in quantum optics such as the quantum Rabi model and the Jaynes-Cummings model and its open-system versions. A theoretical proposal for a trapped-ion experiment to realize the quantum phase transition of the quantum Rabi model will be discussed; moreover, how the motional cooling of an ion could achieve a controlled emergence of the dissipative phase transition from the quantum phase transition.