The silicon-photomultiplier (SiPM) is becoming the device of choice for different applications, for example in fast timing like in time of flight positron emission tomography (TOF-PET) and in high energy physics (HEP). It is also becoming a choice in many single-photon or few-photon based applications, like for spectroscopy, quantum experiments and distance measurements (LIDAR). In order to fully benefit from the good performance of the SiPM, in particular its sensitivity, the dynamic range and its intrinsically fast timing properties it is necessary to understand, quantitatively describe and simulate the various parameters concerned. These analyses consider the structure and the electrical model of a single photon avalanche diode (SPAD), i.e. the SiPM microcell, and the integration in an array, i.e. the SiPM. Additionally, for several applications a more phenomenological and complete view on SiPMs has to be done, e.g. photon detection efficiency, single photon time resolution, SiPM signal response, gain fluctuation, dark count rate, afterpulse, prompt and delayed optical crosstalk. These quantities of SiPMs can strongly influence the time and energy resolution, for example in PET and HEP. Having a complete overview on all of these parameters allows to draw conclusions on how best performances can be achieved for the various needs of different applications.