The development of ambulatory monitoring systems and its electrocardiographic (ECG) signal processing techniques has become an important field of investigation, due to its relevance in the early detection of cardiovascular diseases such as the arrhythmias. The current trend of this technology is oriented to the use of portable equipment and mobile devices such as Smartphones, which have been widely accepted due to the technical characteristics and common integration in daily life. A fundamental characteristic of these systems is their ability to reduce the most common types of noise by means of digital signal processing techniques. Among the most used techniques are the adaptive filters and the Discrete Wavelet Transform (DWT) which have been successfully implemented in several studies. There are systems that integrate classification stages based on artificial intelligence, which increases the performance in the process of arrhythmias detection. These techniques are not only evaluated for their functionality but for their computational cost, since they will be used in real-time applications, and implemented in embedded systems. This paper shows a review of each of the stages in the construction of a standard ambulatory monitoring system, for the contextualization of the reader in this type of technology.