"Those who cannot remember the past, are condemnded to repeat it", Dynamic Programming

Dynamic Programming is a method for solving a complex problem by breaking it down into a collection of simpler subproblems, solving each of those subproblems just once, and storing their solutions using a memory-based data structure (array, map,etc).

Each of the subproblem solutions is indexed in some way, typically based on the values of its input parameters, so as to facilitate its lookup. So the next time the same subproblem occurs, instead of recomputing its solution, one simply looks up the previously computed solution, thereby saving computation time. 

For example, the creation of phylogenetic trees once DNA is known can be tackled easily with Dynamic Programming:

Click here for a complete list of problems that can be solved with Dynamic Programming.