“…After several rounds of revisions and reviewing, seven of the submitted articles were accepted for inclusion in the Special Issue. These seven articles present new results for a wide variety of data compression topics: prefix free codes [1], finding patterns using lossy compression [2], compression in PDE solvers [3], compression and embedding of trees [4], compaction of Church numerals [5], compressed sensing [6], time-universal data compression [7]. Combined these results represent some of the current trends in the field.…”