This chapter explores the philosophical and formal issues surrounding mereological composition. It carefully examines the difference between three main types of fusion: algebraic joins, Leśniewski sums, and Goodman fusions. It also examines different views about their conditions of existence (the so-called ‘special composition question’), including the controversial doctrines of mereological universalism, nihilism, and restricted theories of composition. Next it considers whether fusions are unique and how this impacts extensionality, including presenting a detailed analysis of the thesis known as ‘composition as identity’. A number of ‘structural’ conceptions of composition (and related algebraic principles) are then examined. Finally, parallel to questions about a null object, atomism, and ‘atomless gunk’, the existence of a universal object and the ideas of ‘worldless junk’, and coatomism are considered.