The discovery of atomically thin layered materials such as graphene and transition metal dichalcogenides has unveiled the unique exploration of novel fundamental physics and device applications in two-dimensions. Characterization of their crystal symmetry and subsequent electronic properties are prominent to realize the full potential of these reduced dimensional systems, which fundamentally determine the topology, chirality and rich interfacial physics. Second harmonic generation (SHG), a nonlinear optical effect, is sensitive to crystal symmetry and electronic structures, which proves to be one of the most powerful yet simple technique to capture the essence physics. On the other hand, the 2D nature of layered materials enables large tunability in its physical properties with a number of external stimuli, which in turn paves the way for the development of 2D nonlinear optoelectronic applications. In this review, we overview recent efforts employing second harmonic generation spectroscopy and microscopy to probe lattice structures and dipole polarizations in two-dimensional transition metal dichalcogenide and polar materials. In addition, multiple external stimuli used to control SHG as potential optoelectronic devices are covered. We conclude with a perspective on the future directions of exploration on emerging 2D magnetic and topological materials based on SHG spectroscopy.