Lead halide perovskites have emerged as promising semiconducting materials for different applications owing to their superior optoelectronic properties. Although the community holds different views toward the toxic lead in these high-performance perovskites, it is certainly preferred to replace lead with nontoxic, or at least less-toxic, elements while maintaining the superior properties. Here, the design rules for lead-free perovskite materials with structural dimensions from 3D to 0D are presented. Recent progress in lead-free halide perovskites is reviewed, and the relationships between the structures and fundamental properties are summarized, including optical, electric, and magnetic-related properties. 3D perovskites, especially A(2)B(+)B(3+)X(6)-type double perovskites, demonstrate very promising optoelectronic prospects, while low-dimensional perovskites show rich structural diversity, resulting in abundant properties for optical, electric, magnetic, and multifunctional applications. Furthermore, based on these structure-property relationships, strategies for multifunctional perovskite design are proposed. The challenges and future directions of lead-free perovskite applications are also highlighted, with emphasis on materials development and device fabrication. The research on lead-free halide perovskites at Linkoping University has benefited from inspirational discussions with Prof. Olle Inganas.