This review provides a perspective on the recent developments in the transmission of light through subwavelength apertures in metal films. The main focus is on the phenomenon of extraordinary optical transmission (EOT) in periodic hole arrays, discovered over a decade ago. It is shown that surface electromagnetic modes play a key role in the emergence of the resonant transmission. These modes are also shown to be at the root of both the enhanced transmission and beaming of light found in single apertures surrounded by periodic corrugations. The review describes both the theoretical and experimental aspects of the subject. For clarity, the physical mechanisms operating in the different structures considered are analyzed within a common theoretical framework. Several applications based on the transmission properties of subwavelength apertures are also addressed. EOT is an optical phenomenon in which a structure containing subwavelength apertures in an opaque screen transmits more light than might naively be expected. The phenomenon was discovered serendipitously for two-dimensional (2D) periodic arrays of subwavelength holes in metals. In the original experiments, the holes were milled in optically thick metal films, and the electromagnetic (EM) waves could only tunnel through the apertures in the transmission process. Surprisingly, such arrays may, for certain wavelengths, exhibit transmission efficiencies that exceed unity. This is due to the collective response of the periodic array of holes, which boosts the transmission. The key role played by surface EM modes in the appearance of EOT is now widely recognized. The review discusses the optical properties of individual apertures and arrays of apertures, as well as the transmission properties of single apertures flanked by periodic corrugations. It also addresses several applications based on the transmission properties of subwavelength apertures, including molecular sensing and spectroscopy, photonic devices, and methods. The review concludes with a discussion of the extension of these ideas to other types of waves and future trends. The technical details of the coupled-mode method are presented in the Appendix.This review provides a perspective on the recent developments in the transmission of light through subwavelength apertures in metal films. The main focus is on the phenomenon of extraordinary optical transmission (EOT) in periodic hole arrays, discovered over a decade ago. It is shown that surface electromagnetic modes play a key role in the emergence of the resonant transmission. These modes are also shown to be at the root of both the enhanced transmission and beaming of light found in single apertures surrounded by periodic corrugations. The review describes both the theoretical and experimental aspects of the subject. For clarity, the physical mechanisms operating in the different structures considered are analyzed within a common theoretical framework. Several applications based on the transmission properties of subwavelength apertures are also addressed. EOT is an optical phenomenon in which a structure containing subwavelength apertures in an opaque screen transmits more light than might naively be expected. The phenomenon was discovered serendipitously for two-dimensional (2D) periodic arrays of subwavelength holes in metals. In the original experiments, the holes were milled in optically thick metal films, and the electromagnetic (EM) waves could only tunnel through the apertures in the transmission process. Surprisingly, such arrays may, for certain wavelengths, exhibit transmission efficiencies that exceed unity. This is due to the collective response of the periodic array of holes, which boosts the transmission. The key role played by surface EM modes in the appearance of EOT is now widely recognized. The review discusses the optical properties of individual apertures and arrays of apertures, as well as the transmission properties of single apertures flanked by periodic corrugations. It also addresses several applications based on the transmission properties of subwavelength apertures, including molecular sensing and spectroscopy, photonic devices, and methods. The review concludes with a discussion of the extension of these ideas to other types of waves and future trends. The technical details of the coupled-mode method are presented in the Appendix.