Science is often said to aim at truth. And much of science is heavily dependent on the construction and use of theoretical models. But the notion of model has an uneasy relationship with that of truth.Not so long ago, many philosophers held the view that theoretical models are different from theories in that they are not accompanied by any ontological commitments or presumptions of truth, whereas theories are (e.g. Achinstein 1964). More recently, some have thought that models are not truth-valued at all, but truth-valued claims can be made about similarity relations between models and real systems (e.g. Giere 1988). Others suggest that models are instruments that can be used for attaining truths, for example that models are false means for true theories (e.g. Wimsatt 2007). At the same time, philosophers and others keep talking about models being "correct" and "incorrect", "accurate" and "inaccurate" or getting facts "right" or "wrong". Among practicing scientists, one can find both the notion of a "true model" and the idea that "it is in the nature of models that they are false". There seems to be enough variety of views and confusion around them to invite a little bit of further investigation (see also Mäki 1992, 1994, 2004, 2009a,b,c).