This chapter examines a range of approaches to algorithmic music making inspired by biological systems, and considers topics at the intersection of contemporary music, computer science, and computational creativity. A summary of core precursor movements both within and beyond musical practice (A Life, cybernetics, systems art, etc.) sets the scene, before core models and algorithms are introduced and illustrated. These include evolutionary algorithms, agent-based modelling and self-organizing systems, adaptive behaviour and interactive performance systems, and ecosystemic approaches to composition and computational creative discovery. The chapter closes by reviewing themes for future work in this area: autonomy and agency, and the poetics of biologically inspired algorithms.