A complex chemical mixture is defined as a mixture that consists of tens, hundreds or thousands of chemicals, and of which the composition is qualitatively and quantitatively not fully known. In contrast, a simple mixture consists of a relatively small number of chemicals, say ten or less, and the composition of which is fully known. In the present paper a number of options for hazard identification and risk assessment of complex chemical mixtures is discussed, and a scheme aimed at selecting the most appropriate approach for each (type of) complex mixture is presented. A conspicuous element of this scheme is the dichotomy of complex mixtures into mixtures that are readily available and mixtures that are virtually unavailable for testing in their entirety. Another characteristic aspect of the scheme is the inclusion of the "top-ten" and "pseudo top-ten" approaches, which in essence are ways to select the, say ten, most risky chemicals or pseudocomponents to be dealt with as a simple chemical mixture.