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The discoveries of ferromagnetic and ferroelectric two-dimensional (2D) materials have dramatically inspired intense interests due to their potential in the field of spintronic and nonvolatile memories. This review focuses on the latest 2D ferromagnetic and ferroelectric materials that have been most recently studied, including insulating ferromagnetic, metallic ferromagnetic, antiferromagnetic and ferroelectric 2D materials. The fundamental properties that lead to the long-range magnetic orders of 2D materials are discussed. The low Curie temperature (Tc) and instability in 2D systems limits their use in practical applications, and several strategies to address this constraint are proposed, such as gating and composition stoichiometry. A van der Waals (vdW) heterostructure comprising 2D ferromagnetic and ferroelectric materials will open a door to exploring exotic physical phenomena and achieve multifunctional or nonvolatile devices.