This Perspective outlines basic structural and optical properties of lead halide perovskite colloidal nanocrystals, highlighting differences and similarities between them and conventional II-VI and III-V semiconductor quantum dots. A detailed insight into two important issues inherent to lead halide perovskite nanocrystals then follows, namely, the advantages of defect tolerance and the necessity to improve their stability in environmental conditions. The defect tolerance of lead halide perovskites offers an impetus to search for similar attributes in other related heavy metal-free compounds. We discuss the origins of the significantly blue-shifted emission from CsPbBr3 nanocrystals and the synthetic strategies toward fabrication of stable perovskite nanocrystal materials with emission in the red and infrared parts of the optical spectrum, which are related to fabrication of mixed cation compounds guided by Goldschmidt tolerance factor considerations. We conclude with the view on perspectives of use of the colloidal perovskite nanocrystals for applications in backlighting of liquid-crystal TV displays.