How much time, space and/or hardware resource does require an algorithm? Such questions lead to surprising results: conceptual simplicity does not always go along with efficiency. A lot of quite natural questions remain open, e.g., the famous P \(=\) NP problem raised in 1970. The so elementary model of finite automata, adequately tailored to diverse data structures, proves to be a flexible and powerful tool in the subject whereas quantum computing opens astonishing perspectives. An elegant tool for proofs of lower bounds for time/space complexity is a totally different notion of complexity: Kolmogorov complexity which measures the information contents.