The problem of sequence alignment was introduced around 1970. Since then, many algorithms have been developed, with BLAST being the most famous one. It can quickly reveal similarities between the query sequence and a huge database of sequences. The paper on BLAST came out in 1990, and is currently the most cited paper in history. Nevertheless, sequence alignment is still a very active area of research.
C. Some goals of biology for the next 50 years
In the next 50 years (which is a conservative estimate) the field of molecular biology should be very exciting. Some of the goals including listing all molecular parts that build an organism (genes, proteins, other functional parts), understanding the function of each part, understanding how these parts interact, studying how function has evolved across all species, finding genetic defects that cause diseases, designing drugs rationally, and sequencing the genome of every human to use in personalized medicine. In general, the key is to view biology as information, and to collect and understand this information.
V. Computer scientists vs. biologists
Finally, since bioinformatics is a combination of two fields, biology and computer science, it is interesting to look at the differences between them. First of all, (almost) nothing is ever true or false in biology, while everything is true or false in computer science. Biologists strive to understand the complicated, messy natural world, while computer scientists seek to build their own clean and organized virtual worlds. Biologists are obsessed with being the first to discover something, and computer scientists are obsessed with being the first to invent or prove something. Biologists are comfortable with the idea that all data have errors; computer scientists are not. Finally, computer scientists get high-paid jobs after graduation, and biologists typically have to complete one or more 5-year post-docs... It can be said that computer science is to biology as mathematics is to physics.