Michael Holt's absurdly long and highly detailed "The Rise and Fall of the American Whig Party" is a good read on the subject if you have a few spare months, although Holt is maybe a bit too fond of his Whigs.

The Whig Party was founded in the 1830s as a party opposed to Andrew Jackson in specific and Jacksonian Democracy in general, and like most parties formed in opposition to something, contained many wildly disparate or even contradictory ideologies within it. Some Whigs advocated "internal improvements," or using government funds to build infrastructure like bridges, harbors, and the like, and also advocated for a stronger central government. Others were more interested in opposing popular suffrage (at least at first...the Whig Party eventually came around on universal white male suffrage). The Whigs were deeply torn internally on Westward Expansion (many opposed the Mexican American War in 1846-48) and irrevocably torn on slavery, with the eventual difficult compromise that Northern and Southern Whigs would essentially pretend slavery didn't exist as a political issue in order to continue to get along.

The Whig Party had tremendous difficulty in national elections and could only succeed in two Presidential elections when they were running basically nonideological war hero generals who didn't have much commitment to Whig (or any) political stances: William Henry Harrison in 1840 and Zachary Taylor in 1848 (Taylor famously said that voting for himself in 1848 was the first time he ever voted, period). Both Harrison and Taylor would die in office, and both of their Vice Presidents were, at best, nominally committed to Whig ideas (Fillmore) or, at worst, Democrats passing as Whigs (Tyler, who fired Harrison's entire cabinet). The Whig Party proved incredibly divided as time went on between its Northern half, which was increasingly opposed to the expansion of slavery, and its southern half.

By the 1850s, the relevance of Jacksonian ideology that the Whigs had been founded to oppose began to fade, and with it, the Whigs' issues that had united the party (support of tariffs and internal improvements) took a distant second place to the slavery question. In the North, many Whigs first defected to the Free Soil Party, and then, after 1854, the new Republican Party, which was composed largely (though not totally) of ex-Whigs. Many Southern Whigs defected to the new American Party, sometimes known as the Know-Nothings, which tried to introduce nativist anti-immigrant sentiment as a new unifying national ideology to deflect attention away from slavery.

By the start of the Civil War, the Whig Party was completely defunct (though the Constitutional Union Party, which fell into a humiliating 4th place in the 1860 election, was composed mostly of former Whigs). However, the Whig Party's legacy wasn't completely dead. Because secession was very much the project of the Democratic Party, many ex-Whig politicians in the South, especially in Whig strongholds like North Carolina and Louisiana, proved skeptical at best of the new Confederacy and many were outright Unionists. After the Civil War, many of the "scalawags" (the insulting term used for white Southerners who supported the Republicans and Reconstruction) were ex-Whigs.