First people used to write classifiers by hand, but they found it's too tedious, unreliable and has to redone for each object you want to classify. Then they tried to learn to detect objects by using local feature detector and train a machine learning model to classify objects based on that. This worked much better, but still made some mistakes. Convolutional Neural Network were already used to classify small images of digits, but people were skeptical they would scale to larger images.
This was until in 2012 AlexNet came along. Since then performance of convolutional networks has improved each year. Now they can classify images with similar performance as humans.