Clusters of galaxies, the largest bound objects in the Universe, constitute a cosmological probe of choice, which is sensitive to both dark matter and dark energy. Within this framework, the Sunyaev-Zeldovich (SZ) effect has opened a new window for the detection of clusters of galaxies and for the characterization of their physical properties such as mass, pressure and temperature. NIKA, a KID-based dual band camera installed at the IRAM 30-m telescope, was particularly well adapted in terms of frequency, angular resolution, field-of-view and sensitivity, for the mapping of the thermal and kinetic SZ effect in high-redshift clusters. In this paper, we present the NIKA cluster sample and a review of the main results obtained via the measurement of the SZ effect on those clusters: reconstruction of the cluster radial pressure profile, mass, temperature and velocity.