Biotechnology is emerging as a new driving force for the global economy in the 21st century. An important engine for biotechnology is Bioinformatics. Bioinformatics has revolutionized biology research and drug discovery. Bioinformatics is an amalgamation of biological sciences, computer science, applied math, and systems science. The report provides a brief introduction to molecular biology for non-biologists, with focus on understanding the basic biological problems which triggered the exponentially growing research activities in the bioinformatics fields. The report provides as well a comprehensive literature review of the main challenging problems, and the current tools and algorithms. In particular, the problems of gene modeling, and gene prediction, similarity search, multiple alignments of proteins, and the protein folding problems are highlighted. The report discusses as well how such tools as dynamic programming, hidden Markov models, statistical analysis, clustering, decision trees, fuzzy theory, and neural networks have been applied in solving these problems