Brain-computer interface (BCI) speller is a system that provides an alternative communication for the disable people. The brain wave is translated into machine command through a BCI speller which can be used as a communication medium for the patients to express their thought without any motor movement. A BCI speller aims to spell characters by using the electroencephalogram (EEG) signal. Several types of BCI spellers are available based on the EEG signal. A standard BCI speller system consists of the following elements: BCI speller paradigm, data acquisition system and signal processing algorithms. In this work, a systematic review is provided on the BCI speller system and it includes speller paradigms, feature extraction, feature optimization and classification techniques for BCI speller. The advantages and limitations of different speller paradigm and machine learning algorithms are discussed in this article. Also, the future research directions are discussed which can overcome the limitations of present state-of-the-art techniques for BCI speller.