Silicon photomultipliers (SiPMs) are single-photon sensitive solid-state detectors that are becoming popular for several applications, thanks to massive performance improvements over the last years. Starting as a replacement for the photomultiplier tube (PMT), they are now used in medical applications, big high-energy physics experiments, nuclear physics experiments, spectroscopy, biology and light detection and ranging (LIDAR) applications. Due to different requirements in terms of detection efficiency, noise, etc., several optimizations have been introduced by the manufacturers; for example, spectral sensitivity has been optimized for visible light, near ultraviolet, vacuum ultraviolet, and near infrared light. Each one of them require specific processes and structural optimization. We present in this paper recent improvements in SiPM performance, owing to a higher cell fill-factor, lower noise, improved silicon materials, and deep trench isolation. We describe issues related to the characterization of analog SiPM, particularly due to the different sources of correlated noise, which have to be distinguished from each other and from the primary pulses. We also describe particular analyses and optimizations conducted for specific applications like the readout of liquid noble gas scintillators, requiring these detectors to operate at cryogenic temperatures.