Short answers, pulled from the story.
The Radical Republicans were a faction within the Republican Party that called for the immediate, complete, and permanent eradication of slavery in the United States. They also demanded full civil rights and voting rights for freed slaves, a harsh Reconstruction of the Confederate South, and strong federal enforcement of those rights against Southern resistance.
The most influential Radical Republican leaders in Congress were Thaddeus Stevens, a representative from Pennsylvania, in the House, and Charles Sumner, a senator from Massachusetts, in the Senate. Stevens was described as the Radicals' most successful and systematic leader.
The Radical Republicans believed Lincoln was too slow to free enslaved people and too lenient in his terms for readmitting Southern states. They opposed his veto of the Wade-Davis Bill in 1864 and rejected his plan to compensate slave owners who had stayed loyal to the Union, demanding instead uncompensated abolition.
The Radical Republicans impeached Johnson after he violated the Tenure of Office Act by dismissing Secretary of War Edwin M. Stanton. The House voted 126-47 to impeach him. The Senate held three separate votes, each returning 35-19, one short of the 36 votes needed for conviction, so Johnson was acquitted in 1868.
The Radical Republican era effectively ended with the Compromise of 1877. Republican Rutherford B. Hayes won the disputed 1876 presidential election by securing the electoral votes of Louisiana, Florida, and South Carolina, then withdrew federal troops from those states. Without military protection, Reconstruction governments immediately collapsed and the period of Jim Crow laws began.
Early 20th-century Dunning School historians at Columbia University portrayed the Radicals as corrupt power-seekers who imposed misrule on the South. In the 1930s, revisionist historians including W.E.B. Du Bois and C. Vann Woodward rejected that view but cast the Radicals as economic opportunists. Since the 1950s, scholars influenced by the Civil Rights Movement have emphasized the Radicals' genuine achievements in civil rights and Black suffrage as more significant than the era's corruption.