The core strategy to faster product development projects so as to gain competitive advantage consists in overlapping development stages so the downstream stage can start earlier by using preliminary information. Quality issues implied by overlapping are resolved using rework to correct design flaws resulting from partial information. Thus for such projects, quality is implicitly taken into account with rework (see for instance Lin et al., 2010 for a recent contribution). Besides, to accelerate non innovative projects so as to ensure delivery on the planned date, some of the project activities can be completed faster than normal by either spending less time on them or more money to cover the expenses of additional resources allotted to them. Thus accelerating a project increases its cost. As it is commonly assumed that shortening the duration of activities decreases their quality and consequently the project quality, there is a tradeoff between time, cost and quality. Most of Time Cost Quality Trade-off Problems (TCQTP) are modelled in a similar way to Time Cost Trade-off Problems (TCTP) that have been extensively studied in the literature related to deterministic project scheduling (see Weglarz et al., 2011 for a recent survey). As such, they share common assumptions that we discuss in this survey to provide a grid for classifying TCQTP. In TCQTP studied here, quality of any activity is measured by an indicator varying between 0 and 1 and so is the overall project quality for it is defined as a function of quality levels attained by individual activities. We analyse the meaning of such an indicator, its acceptable level as well as aggregation methods used to derive the project quality. The remainder of this paper is organised as follows. Section 2 discusses the definition and measure of quality and analyses the impact of acceleration on quality. Section 3 provides a classification of TCQTP based upon modelling assumptions and solution methods, which eventually led us to identify three main approaches. In the first one, quality is implicitly assessed through rework needed to correct non conforming activities (Section 4). In the second one, the quality of any activity is expressed as a continuous function of its duration and cost (Section 5). In the last group of references, quality of an activity is estimated in each of its possible execution modes, a mode corresponding to a specific combination of resources to process the activity with an associated duration and cost. Section 7 provides a summary of the contributions in terms of resource category, activity quality and project quality definitions, solution approaches and project instances being addressed.