The study of what will happen when all things are consummated at the end of history is called eschatology. That word comes from two Greek words, eschatos (last) and logos (the expression of thought). So eschatology is the expression of thought of last things.
The Biblical discussion of the last days begins in Joel 2:28-29 where he's predicting the coming of the Holy Spirit and he says it will come to pass "afterward." That Hebrew word means "the hind part." Joel is saying the Holy Spirit will come in the last days. Peter verifies this in his sermon at Pentecost. Acts 2:16-17a says, "But this is that which was spoken by the prophet Joel; And it shall come to pass in the last days, saith God, I will pour out my Spirit upon all flesh……" These "last days" are spoken of numerous times in the New Testament, for example see I Timothy 4:1, I Peter 1:20, & I John 2:18.
Most people seem to think of the last days as the time in history just before the rapture of the church, or the period of the great Tribulation just before the 1,000-year Kingdom-Age begins.
Actually, it appears that the "last days" began officially at Pentecost, 50 days after Jesus was crucified, when the prophecy of Joel was fulfilled. Paul warns Timothy (2 Timothy 3:1), "in the last days perilous times shall come." He goes on with a list of perverse human behavior that will be prevalent in the last days. The word perilous is chalepos (khal-ep-os') and it means hard to do or deal with, difficult, fierce, perilous. This word is used only twice in the Bible, once describing the devils in the Gadarene man (Matthew 8:28) and of the last times (2 Timothy 3:1)
So we've been in the last days for almost 2,000 years, and if you read what Paul told Timothy to expect (2 Timothy 3:2-8), just as most things deteriorate over time, the last days have too. In our day it's hard to imagine any last day prophecy that isn't happening on a routine basis. We've concentrated on "wars and rumors of wars," but all the other predictions are common happenings in our 21st Century world. I think we can safely say we're nearing the end of the last days.
Dr. Schofield makes a distinction between the last days as they relate to the church and the last days as they relate to Israel. For the church the last days began at Pentecost and will end when The Lord physically returns to The Mount of Olives outside Jerusalem at the end of the Tribulation. For Israel, he says the last days refer to Israel's exaltation and blessing during the 1,000-year Kingdom-Age, when all of the unconditional promises made to Abraham will be fulfilled.