Understanding the limit of algorithms in solving hard optimization combinatorial problems is a fundamental problem both in basic research and real-world applications. However, results are scarce, especially for sparse models, which are the most realistic ones. I will summarize our current understanding of algorithmic thresholds in well-known problems, like satisfiability and coloring, focusing mainly on the dependence of algorithmic thresholds on the time scaling and on the analytical attempts to estimate these thresholds.