Insights at the microscopic level of the process of radiocesium adsorption and interaction with clay mineral particles have improved substantially over the past several years, triggered by pressing social issues such as management of huge amounts of waste soil accumulated after the Fukushima Dai-ichi nuclear power plant accident. In particular, computer-based molecular modeling supported by advanced hardware and algorithms has proven to be a powerful approach. Its application can now generally encompass the full complexity of clay particle adsorption sites from basal surfaces to interlayers with inserted water molecules, to edges including fresh and weathered frayed ones. On the other hand, its methodological schemes are now varied from traditional force-field molecular dynamics on large-scale realizations composed of many thousands of atoms including water molecules to first-principles methods on smaller models in rather exacting fashion. In this article, we overview new understanding enabled by simulations across methodological variations, focusing on recent insights that connect with experimental observations, namely: 1) the energy scale for cesium adsorption on the basal surface, 2) progress in understanding the structure of clay edges, which is difficult to probe experimentally, 3) cesium adsorption properties at hydrated interlayer sites, 4) the importance of the size relationship between the ionic radius of cesium and the interlayer distance at frayed edge sites, 5) the migration of cesium into deep interlayer sites, and 6) the effects of nuclear decay of radiocesium. Key experimental observations that motivate these simulation advances are also summarized. Furthermore, some directions toward future solutions of waste soil management are discussed based on the obtained microscopic insights.