Metal additive manufacturing (AM) has been extensively studied in recent decades. Despite the significant progress achieved in manufacturing complex shapes and structures, challenges such as severe cracking when using existing alloys for laser powder bed fusion (L-PBF) AM have persisted. These challenges arise because commercial alloys are primarily designed for conventional casting or forging processes, overlooking the fast cooling rates, steep temperature gradients and multiple thermal cycles of L-PBF. To address this, there is an urgent need to develop novel alloys specifically tailored for L-PBF technologies. This review provides a comprehensive summary of the strategies employed in alloy design for L-PBF. It aims to guide future research on designing novel alloys dedicated to L-PBF instead of adapting existing alloys. The review begins by discussing the features of the L-PBF processes, focusing on rapid solidification and intrinsic heat treatment. Next, the printability of the four main existing alloys(Fe-, Ni-, Al- and Ti-based alloys) is critically assessed, with a comparison of their conventional weldability. It was found that the weldability criteria are not always applicable in estimating printability. Furthermore, the review presents recent advances in alloy development and associated strategies, categorizing them into crack mitigation-oriented, microstructure manipulation-oriented and machine learning-assisted approaches. Lastly, an outlook and suggestions are given to highlight the issues that need to be addressed in future work.