Cancer is a disease whose process is characterized by the accumulation of somatic alterations to the genome, which selectively make a cancer cell fitter to survive. The understanding of progression models for cancer, i.e., the identification of sequences of mutations that leads to the emergence of the disease, is still unclear. The problem of reconstructing such progression models is not new; in fact, several methods to extract progression models from cross-sectional samples have been developed since the late 90s. Recently, we have proposed a number of algorithms to reconstruct cancer progression models both from aggregate, population level data -- i.e., collections of patients' data, as many TCGA datasets --- and from individual level data -- i.e., single tumor, or even single cell data. We perform the reconstruction by exploiting the notion of probabilistic causation in the spirit of Suppes’ causality theory. We note that in the context of biological systems and cancer progression, the notion of causality can be interpreted as the notion of "selective advantage" of the occurrence of a mutation. In this setting, we have proven the correctness of our algorithms and characterized their performance. Our algorithms are collected in a R BioConductor package "TRanslational ONCOlogy" (TRONCO) that we have successfully used as part of our "Pipeline for Cancer Inference" (PiCnIc) to analyse Colorectal Cancer (CRC) data from TCGA, which highlighted possibly biologically significant patterns in the progressions inferred. To conclude the presentation, we will present some novel applications of our algorithm suite and of our pipeline to other TCGA datasets and list some new developments for individual tumour analysis.