Electromagnetic metasurfaces, as a class of planar electromagnetic materials consisting of single-layer or multilayer subwavelength artificial micro-structures, can precisely control the amplitude, phase, wavefront, dispersion, polarization, and angular momentum of electromagnetic waves in the subwavelength scale. In particular, reflectionless electromagnetic metasurfaces provide new theories and schemes for realizing high-efficiency electromagnetic devices. In this review, we elaborate the underlying mechanism of reflectionless metasurfaces from the perspective of the Huygens principle, electromagnetic resonances and the Brewster effect. We also discuss the important applications including anomalous refraction, polarization manipulation, meta-antireflection coatings, and perfect electromagnetic absorption, and point out the challenges and potentials of this field.