In the early to mid 1900's pitchers were throwing 300+ innings in a season. Going the distance (pitching 9 or more innings) was the norm and pitchers would do it because they would take pride in throwing all them innings. Now a days pitchers that get over 200 innings is a workhorse. Justin Verlander won an MVP and a Cy Young with 250 innings pitched in his 34 games started. This year Clayton Kershaw is having his dominant year and is already at 209 innings which leads the National League and ultimately is going to win him the Cy Young and maybe even the MVP (depending on who you talk to) for this year, but the old school workhorses used to look at the innings now and laugh because those innings numbers would have been in mid to late August for them.
What has changed, well money. Clayton Kershaw is making 11 million dollars this year and is going to break the bank this off season when he is set to become a free agent. Justin Verlander made 12.850 million when he won his MVP and is making upwards of 20 million now. As the philosophies of teams have changed to pitching and playing better defense pitcher's salaries have been on the rise. Now a days if you're a perennial Cy Young candidate or just win one Cy Young you'll probably leave a bank somewhere with heavy pockets. RA Dickey won a Cy Young with the New York Mets in 2012 while making 4.25 million dollars he was traded after the year to the Toronto Blue Jays where at the end of his current deal he's going to be making 12 million dollars a season.
How are innings being cut back, well in today's baseball game a pitcher is asked to go at the very least 7 innings (if the team has an average bullpen) or throw 100 pitches whichever comes first. Once the 7th inning arrives you'll see a reliever in the game to go either one inning or one hitter (if he's a specialist). After that reliever then comes another reliever for the 8th inning and the closer for the 9th (if there is a save situation). There are ways a pitcher can end a game he begins; if there is a perfect game (9 innings, no hits, no runs), a no hitter (9 innings, no hits, no runs, but a few walks) or if there are chances to rest the pitcher in the weeks ahead or he was economical while he was in the game (to the point where he didn't reach the 100 pitches by the 7th inning or later). The more scarcer situation is if the bullpen needs a rest, then no matter what the pitcher may be out there to throw 9 innings that's when a pitcher is going to have to "bear it" so even if he's getting rocked he'll stay on that mound until the manager can't take it anymore then he'll try to find the freshest arm to then remove the starting pitcher.
With salaries for pitchers being this high organizations want to keep their pitchers on the mound so the innings are being cut back little by little. With more pitches being thrown there are bigger chances for a pitcher to get hurt and with the dread Tommy John surgery (named after pitcher Tommy John who was the first player to get the surgery where doctors replace the deteriorated ulnar collateral ligament in the elbow) out there organizations don't want to the risk of losing any of their pitchers especially their "ace" for a whole year (which is typically the amount of time it takes to recover from Tommy John surgery).