This series of working papers explores a theme enjoying a tremendous resurgence: the functional distribution of income - the division of aggregate income by factor share. This first installment surveys some landmark theories of income distribution. Some provide a technology-based account of the relative shares while others provide a demand-driven explanation (Keynes, Kalecki, Kaldor, Goodwin). Two questions lead to a better understanding of the literature: is income distribution assumed constant?, and is income distribution endogenous or exogenous? However, and despite their insights, these theories alone fail to fully explain the current deterioration of income distribution. Subsequent installments are dedicated to analyzing the empirical literature (part II), to the measurement and composition of the relative shares (part III), and to a study of the role of economic policy (part IV).