## 1 Introduction  
When sound is reproduced by one or more loudspeakers, the perception of the desired auditory illusion is modified by the listening environment. To some extent this may be seen as positive, since spaciousness and depth is added, but the environment and the sound reproduction system can also introduce undesired artifacts. Excessive reflections or resonances within the listening environment may result in an undesired alteration of the auditory illusion. A non-ideal reproduction system may even add some artifacts (e.g., frequency band extension, nonlinearities) to the original sound. Room response equalization (RRE) has been studied in theory and applied in practice for improving the quality of sound reproduction contrasting the detrimental effects of the room environment and reproduction system. In an RRE system, the room transfer function (RTF) characterizing the path from the sound reproduction system to the listener is equalized with a suitably designed equalizer that can be realized in several manners. The basic idea is to measure the room impulse response (RIR) using a microphone, and then obtain the equalizer through its inversion. However, several issues influence this method, and thus a wide variety of techniques have been developed over the last 40 years. The reader should be aware that many different names have been used in the literature for RRE, such as \"room equalization\", \"room correction\", \"room compensation\", \"room inversion\", \"room dereverberation\", \"dereverberation\", \"reverberation reduction\", and others. In this review, the collective term RRE is used to denote any technique that aims to design an equalizer from measurements of the RTF. Borrowing the words of [1], there is a \"_multidimensionality of alternatives for room inverse filter design\"_. In particular, the inversion of the RIR can be performed considering a non-parametric approach such as least-mean-squares or direct inversion of the frequency response [1; 2], a parametric approach such as autoregressive-moving average (ARMA) modeling [1; 3], or temporal decay control at low frequency [1; 4]. However, as reported in [1], this is not the only classification possible: RRE can also be classified into minimum- or mixed-phase. The former aims only at the equalization of RTF magnitude, while the latter also acts on the excess-phase RTF component. In this review paper, a general classification is presented aiming at a broader view on the state-of-the-art in RRE. Figure 1 provides a conceptual scheme of this classification, clustering the various techniques that will be presented in the following. As shown in Figure 1, the RRE approaches are divided into single-point (single-input/single-output--SISO, multiple-input/single-output--MISO) and multi-point (single-input/multiple-output--SIMO, multiple-input/multiple-output--MIMO) room equalizers. A single position room equalizer estimates the equalization filter on the basis of the measurement in a single location of the RTF [5]. It is effective only in a limited zone around the measured point (of the size of a fraction of the acoustic wavelength). In reality, the RTF varies significantly with respect to the position in the room [6; 7] and time [2], as the room can be considered a _\"weakly non-stationary\"_ system [8]. To enlarge the equalized zone and to contrast the room response variations, multi-point equalizers have been proposed [9]. A multi-point room equalizer uses multiple measurements of the RTF at different locations in order to design the equalizer. These approaches can be used for fixed and adaptive equalization. The former is based on RTFs measured at fixed positions at a certain time. The latter is capable of tracking and adapting to changes in the room response due to its time varying nature resulting for instance from temperature changes or movement of people or other obstacles. Different pre-processing techniques are applied to contrast audible distortions caused by fixed equalization in scenarios where RTFs vary.