Diamond thin films have outstanding optical, electrical, mechanical and thermal properties, which make these attractive for applications in a variety of current and future systems. In particular, the wide band gap, optical transparency and unusually high thermal conductivity of diamond thin films make them an ideal semiconductor for applications in current and future electronics. However, synthesis of diamond thin films with adequate quality remains a challenging task. Synthesis of diamond at low temperatures is even more challenging because of the difficulties in the nucleation and growth steps involved in diamond thin film deposition on a variety of substrates. Among the several deposition techniques for synthesising diamond films, plasma enhanced chemical vapour deposition is the most promising technique because of its potential for low temperature synthesis. Consequently, the first part of this paper reviews the current state of the nucleation and growth of diamond during chemical vapour deposition. A uniform and high nucleation density is a prerequisite for getting a good quality diamond film with significant growth rate. Also, since the process conditions for nucleation and growth steps are different, attempts are made in this review to identify the important parameters responsible for enhancing the nucleation and growth rates of diamond film. Describing the indispensable need for low temperature growth of diamond film, the second part of the paper reviews the research on the growth of diamond thin films at low temperatures. In spite of the slower kinetics at lower deposition temperatures, an attempt is made to identify the key processing conditions, which enhance the low temperature growth process. In addition, the mechanisms of diamond nucleation and growth are discussed based on the observations from in situ characterisation techniques such as Fourier transform infrared reflection absorption spectroscopy, real time spectroscopic ellipsometry and molecular beam mass spectroscopy.