In the past few years, the demand for high data rate services has increased dramatically. The congestion in the radio frequency (RF) spectrum (3 kHz ~ 300 GHz) is expected to limit the growth of future wireless systems unless new parts of the spectrum are opened. Even with the use of advanced engineering, such as signal processing and advanced modulation schemes, it will be very challenging to meet the demands of the users in the next decades using the existing carrier frequencies. On the other hand, there is a potential band of the spectrum available that can provide tens of Gbps to Tbps for users in the near future. Optical wireless communication (OWC) systems are among the promising solutions to the bandwidth limitation problem faced by radio systems. In this paper, we give a tutorial survey of the most significant issues in OWC systems that operate at short ranges such as indoor systems. We consider the challenging issues facing these systems such as (i) link design and system requirements, (ii) transmitter structures, (iii) receiver structures, (iv) challenges and possible techniques to mitigate the impairments in these systems, (v) the main applications and (vi) open research issues. In indoor OWC systems we describe channel modelling, mobility and dispersion mitigation techniques. Infrared communication (IRC) and visible light communication (VLC) are presented as potential implementation approaches for OWC systems and are comprehensively discussed. Moreover, open research issues in OWC systems are discussed.