Blue Large-Amplitude Pulsators (BLAPs) are a recently discovered class of short-period pulsating variable stars. In this work, we present new information on these stars based on photometric and spectroscopic data obtained for known and new objects detected by the OGLE survey. BLAPs are evolved objects with pulsation periods in the range of 3--75 min, stretching between subdwarf B-type stars and upper main-sequence stars in the Hertzsprung-Russell diagram. In general, BLAPs are single-mode stars pulsating in the fundamental radial mode. Their phase-folded light curves are typically sawtooth shaped, but light curves of shorter-period objects are more rounded and symmetric, while many longer-period objects exhibit an additional bump. The long-term OGLE observations show that the period change rates of BLAPs are usually of the order of 10^-7 per year and in a quarter of the sample are negative. An exception is the triple-mode object OGLE-BLAP-030, which changes its dominant period much faster, at a rate of about +4.6 x 10^-6 per year. The spectroscopic data indicate that the BLAPs form a homogeneous group in the period, surface gravity, and effective temperature spaces. However, we observe a split into two groups in terms of helium-to-hydrogen content. The atmospheres of the He-enriched BLAPs are more abundant in metals (about five times) than the atmosphere of the Sun. We discover that the BLAPs obey a period--gravity relationship and we use the distance to OGLE-BLAP-009 to derive a period--luminosity relation. Most of the stars observed in the OGLE Galactic bulge fields seem to reside in the bulge, while the remaining objects likely are in the foreground Galactic disk.