In this paper, we study the unicity of meromorphic functions and their differential-difference polynomials. Our results improve some results due to Chen-Yi [Results Math 63 (2013):557-565], Chen-Xu [Open Math 18 (2020):211-215], Banerjee-Maity [Bull Korean Math Soc 58 (2021):1175-1192], and Narasimha-Shilpa [Adv Pure Appl Math 13 (2022):53-61] [ABSTRACT FROM AUTHOR]