The aim of this work is to present an overview and a critical discussion on two-dimensional materials and functional nanostructures exhibiting ferromagnetic and antiferromagnetic long-range ordering at or above room temperature. We specially describe and discuss the series of results concerning two-dimensional magnetism originated from intrinsic and induced d magnetic moments in low-dimensional nanostructured materials. Selected materials showing two-dimensional magnetic properties close to room temperature are classified as atomic monolayers, natural and artificial van der Waals layers, magneto-lamellar intermetallic compounds, and nanostructured materials containing native and artificially created defects that originate magnetic moments in networks with two-dimensional interconnectivity. To make the point on these materials, we describe their atomic and electronic structures as well as magnetic interaction mechanisms responsible for magnetic behavior. Theoretical backgrounds for understanding the correlations between structure and magnetic properties are examined. Special emphasis on the possible applications of two-dimensional magnetism for developments of new devices in the fields of spintronics, spin-orbitronics, magnonics, valleytronics and twistronics, among other emergent technologies are discussed.