Despite advances in algorithms and computational platforms, de-novo genome assembly remains a challenging process. Due to the constant innovation in sequencing technologies (Sanger, SOLiD, Illumina, 454, PacBio and Oxford Nanopore), genome assembly has evolved to respond to the changes in input data type. This paper includes a broad and comparative review of the most recent short-read, long-read and hybrid assembly techniques. In this review, we provide (1) an algorithmic description of the important processes in the workflow that introduces fundamental concepts and improvements; (2) a review of existing software that explains possible options for genome assembly; and (3) a comparison of the accuracy and the performance of existing methods executed on the same computer using the same processing capabilities and using the same set of real and synthetic datasets. Such evaluation allows a fair and precise comparison of accuracy in all aspects. As a result, this paper identifies both the strengths and weaknesses of each method. This comparative review is unique in providing a detailed comparison of a broad spectrum of cutting-edge algorithms and methods.