This train is one of the oldest, continuously running trains in India. While not as popular as it's 'legendary' sister, the 'Punjab mail', it was a highly patronized, important train before independence.
This train was started as a third-class-only express between Delhi and Bombay Victoria Terminus (BBVT or CSTM) from 1st February, 1907. From 1st September, 1919, it started carrying passengers of all classes (1st, 2nd, Inter and 3rd). From that point onward, it proved to be a very popular train with the passengers. At the time, this was simply called the G.I.P Delhi Express (G.I.P stands for Great Indian Peninsular Railway, the predecessor of CR, WCR, parts of NCR, NR and SCR).
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1919, the Punjab mail used to depart from Bombay at 1PM in the afternoon, reaching Delhi the next night at 8PM. The Delhi express on the other hand, was slower, but had more convenient timings, departing from Bombay around 10PM and reaching Delhi around 8AM on the third morning. It was slower than the Punjab mail by about three hours, but was highly preferred because of the 2-night, 1-day schedule.
In the mid 1920's, the train was extended gradually to Lahore and further to Rawalpindi and Peshawar, before being terminated at Lahore. For a few months after the introduction of the Mangalore-Peshawar Grand Trunk express (12615/16) , the Mangalore-Peshawar through coaches were attached to the Delhi express between Itarsi and Delhi.
From 1st March, 1931, it was extended to Peshawar. From this time onward, it was popularly known as the "G.I.P Peshawar express". The train used to run via Meerut, Saharanpur between Delhi and Lahore. It used to run with the numbers 197/198 on the GIPR till Delhi and as 57/58 onward to Peshawar (It still carries the 57/58 numbers to this day, as 11057/58).
By 1943, due to the world war, rail traffic on all the lines was severely affected. During this time, the Peshawar express was diverted to run via Karnal, Panipat, Ambala; the same route it takes today.
At the time of partition, it was terminated at Delhi, with a connecting train running between Delhi-Amritsar. A few years later, it was extended to Pathankot via Amritsar. During this time, the train became famous as "Pathankot express". The train and the name were extremely popular and even to this day, most railway officials and documents refer to the 11057/58 as Pathankot express.
From 1st April, 1968, the train was short-terminated at Amritsar (a passenger shuttle service was introduced between Pathankot and Amritsar to replace this train), and a few years later, the terminal was changed to Dadar.

Timeline:
1st Feb 1907: 27/28 Delhi Express (2nd Class). in 1918, 30 Exp can be seen in Image.
1st Sep 1919: 27/28 (maybe 29/30) diverted ALD as Bombay Exp. GIP Delhi Express introduced as Peshawar/Luckow Exp (Through Link Service to LKO via JHS & Peshawar via DLI)
1947: Dufferin Bridge reconstructed (commenced in 1942) to handle double track, name changed to Malviya Bridge (1947),...
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Bombay Exp diverted to Benaras as Kashi Exp.
1990: Kashi Exp extended to GKP past GC!!