Accelerating the discovery of low-dimensional materials having improved properties and advanced capabilities are essential in the 21st century to enable future development of nanotechnology in challenge applications such as flexible electronics, portable sensors, solar panels, photodiodes, phototransistors, tunneling devices, etc. Experimental and computational simulating methodologies, as well as machine learning, developed recently, are mainstream routes to explore nanomaterials. In this talk, I will focus on the computational discovery and design of low-dimensional materials by employing first-principles and semi-empirical methods. The routes in predicting new nanomaterials and methods used in computational simulations will be discussed. I will present our recent theoretical predictions on low dimensional materials as examples including (1) boron structures based on icosahedron B12, (2) SiC nanowires and sheets, and (3) sandwiched two-dimensional phosphide binary compounds sheets. The structural optimizations and analyses of structural properties will be discussed. At the end, I will briefly talk about our ongoing work on the discovery of blue phosphorene with Li intercalation and design of lateral heterostructures formed by two-dimensional SiC and GeC sheets.