Chromosomal instability (CIN), an increased rate of chromosomal segregation abnormalities, drives intratumor heterogeneity and affects most human cancers. In addition to chromosome copy number alterations, CIN results in chromosome(s) (fragments) being mislocalized into the cytoplasm in the form of micronuclei. Micronuclei can be detected by cGAS, a double-strand nucleic acid sensor, which will lead to the production of the second messenger 2′3′-cGAMP, activation of an inflammatory response, and downstream immune cell activation. However, the molecular network underlying the CIN-induced inflammatory response is still poorly understood. Furthermore, there is emerging evidence that cancers that display CIN circumvent this CIN-induced inflammatory response, and thus immune surveillance. The STAT1, STAT3, and NF-κB signaling cascades appear to play an important role in the CIN-induced inflammatory response. In this review, we discuss how these pathways are involved in signaling CIN in cells and how they are intertwined. A better understanding of how CIN is being signaled in cells and how cancer cells circumvent this is of the utmost importance for better and more selective cancer treatment.