Alenza was born in Madrid and lived there throughout his life. As a young man he learned the basics of drawing from Juan Antonio de Ribera and at the classes given by José de Madrazo at the Real Academia de Bellas Artes de San Fernando. Having completed his artistic training he soon began to receive official commissions. Alenza is considered to be one of the Spanish artists most influenced by Goya, from whom he derived a taste for the depiction of the socially marginalised and condemned individuals and the use of a muted, greyish-brown tonal range. He was also a tireless draughtsman and it was his passion for drawing everything around him that has made him the great narrator of the habits and customs of the popular classes and the urban poor in the Madrid of his time.