Quickselect
Also known as: Hoare's selection algorithm, Quick select
Quickselect finds the $k$-th smallest element (order statistic) using the same partition step as quicksort, but recurses into only one side.
Average time $O(n)$; worst case $O(n^2)$ with bad pivots. Expected linear time with random pivots is the usual practical claim. A heap also solves top-$k$ problems, with different constants and a clearer worst case for the heapify path.
Use when you need one order statistic, not a full sort. Median-of-medians gives deterministic linear worst case but is rarely what you ship.