This review concerns how cytoplasmic mRNA half-lives are regulated and how mRNA decay rates influence gene expression. mRNA stability influences gene expression in virtually all organisms, from bacteria to mammals, and the abundance of a particular mRNA can fluctuate manyfold following a change in the mRNA half-life, without any change in transcription. The processes that regulate mRNA half-lives can, in turn, affect how cells grow, differentiate, and respond to their environment. Three major questions are addressed. Which sequences in mRNAs determine their half-lives? Which enzymes degrade mRNAs? Which (trans-acting) factors regulate mRNA stability, and how do they function? The following specific topics are discussed: techniques for measuring eukaryotic mRNA stability and for calculating decay constants, mRNA decay pathways, mRNases, proteins that bind to sequences shared among many mRNAs [like poly(A)- and AU-rich-binding proteins] and proteins that bind to specific mRNAs (like the c-myc coding-region determinant-binding protein), how environmental factors like hormones and growth factors affect mRNA stability, and how translation and mRNA stability are linked. Some perspectives and predictions for future research directions are summarized at the end.