A $k$-plex is a graph theoretic generalization of a clique, introduced in social network analysis (SNA) to model tightly knit social subgroups referred to as cohesive subgroups. Clique model was the earliest mathematical model for a cohesive subgroup, but its overly restrictive definition motivated several relaxations including the $k$-plex model. The models from SNA are suitable, and potentially more realistic cluster models for graph-based clustering and data mining. This article will discuss the applicability of the $k$-plex model and its advantages compared to the clique model. Some recent developments in integer programming based approaches to identify large $k$-plexes would be described and the approaches demonstrated on a text mining network.