Group-10 transition metal chalcogenides (such as PtS₂, PtS, PdS₂, PtSe₂, PdSe₂, PtTe₂, Pt₂Te₃ and PdTe₂) have attracted increasing attention owing to their strong spin-orbit coupling, thickness-dependent band structures, and promising applications in electronics, optoelectronics, spintronics, and energyrelated devices. Recent advances in growth techniques particularly molecular beam epitaxy (MBE), chemical vapor deposition (CVD), and thermal assisted conversion (TAC) have enabled the controllable synthesis of high-quality two-dimensional chalcogenide films. However, a systematic review focusing on the growth of transition metal chalcogenides especially from the perspective of MBE remains lacking. This work is dedicated to filling this gap by providing a comprehensive overview of MBE growth strategies and key parameters as well as other mainstream methods for Group-10 transition metal dichalcogenides (TMDCs) and furthermore, the broader family of Pt- and Pd- based chalcogenides, exploring the growth, phase control, and unique properties of various stoichiometric phases. This review also summarizes their representative physical properties and emerging device applications, aiming to fill the gap in the literature on MBE growth of transition metal chalcogenides and to provide guidance for the controllable synthesis and device integration of high-quality two-dimensional chalcogenide materials.