I will discuss the efficient computation of the Vietoris–Rips persistence barcode for a finite metric space. The implementation in the C++ code „Ripser“ focuses on memory and time efficiency, outperforming previous software on typical benchmark examples both in terms of time and memory. The improved computational efficiency is based on a close connection between persistent homology and discrete Morse theory, together with novel algorithmic design principles, avoiding the explicit construction of the filtration boundary matrix.