This paper discusses the need for on-chip correction of mixed-signal integrated circuits, and particularly Analog-to-Digital Converters (ADCs), for in-situ adaptation to the operating conditions. By operating conditions, we mean the environmental conditions and the electrical settings applied to the ADC by the complex system in which it is implemented. This discussion is supported by experimental measurements of the impact of temperature and sampling frequency on the non-linearity of the ADC and its correction using a so-called LUT-based (Look-Up Table) correction technique. These experimental results enlighten the need for in-situ correction and an architectural solution is presented. The feasibility of this solution is discussed in terms of silicon area overhead and LUT-filling time.