In this paper, the concept of Pythagorean fuzzy compactness, Pythagorean fuzzy almost compactness and Pythagorean fuzzy near compactness are introduced and studied. We give some characterizations of Pythagorean fuzzy almost compactness in terms of Pythagorean fuzzy regular open or Pythagorean fuzzy regular closed. Also, we investigate the behavior of Pythagorean fuzzy compactness under several types of Pythagorean fuzzy continuous.