Open star clusters (OCs) represent an important constituent of the disc in the Milky Way and in other galaxies. Each OC is made of a single/simple stellar popualation (SSP = one age, one metallicity) and provides a direct insight to the stellar initial mass function, stellar evolution, and the age-metallicity relation of the disc. The age distribution of the OC sample in the extended solar neighbourhood is well defined, while the cluster masses are very uncertain due to incompleteness, field contamination and the impact of unresolved binaries on the velocity dispersion. Gaia DR2 data promise a significant step forward concerning cluster membership leading to improved cluster properties including the observation of tidal tails. In order to determine the fraction of field stars formed in OCs detailed dynamical models are needed. I will discuss different aspects of OCs based on our analytical and numerical investigations including initial conditions, cluster lifetimes, cluster sizes and the structure of tidal tails. Our goal is to provide detailed models of individual OCs and to convert the observed cluster age-mass distribution to a cluster formation rate and cluster initial mass function.