The insurgency traces its origins back to the era directly following the period known as La Violencia (the political conflict between the Liberal and Conservative parties after the murder of Liberal leader and general strongman Jorge Eliécer Gaitán in 1948), which eventually resulted in the ousting of pseudo-fascist President Laureano Gómez by a coalition of moderate forces of both parties and the National Army. After a four-year "dictatorship" (not really) that was ostensibly non-partisan, the two parties once again realised that the dictator, Gustavo Rojas Pinilla, was a bit too much for them to hold, especially since Rojas Pinilla was definitely in the left wing of things. In Spain, they agreed to share power to oust other political currents from government, something called the National Front; where a coalition of the two parties was arranged so that the Presidency was shared in four-year terms (one Liberal must always be followed by one Conservative) and the legislature (and even judicial appointments) were split equally amongst both parties.
While ostensibly returning democracy to Colombia (free and fair elections returned to the nation in 1958, the first to count with woman's suffrage), the National Front was of course a bit of a destruction of the traditional order of Colombian politics and forced a lot of smaller movements to keep quiet. The left, led by Gustavo Rojas Pinilla in the polls, was the first to suffer. Armed bands of leftists had for a long time inhabited several areas of the country, but push came to shove when, in 1964, the Colombian army bombed and invaded a leftwing redoubt called Marquetalia. After this, a new military organisation, the FARC, were born.
The FARC were, for most of their history, outshined by another, larger terrorist organisation; the April-19 Movement (M-19), which was founded after the 1970 election, which was seen as a sure victory for Rojas Pinilla and as a defeat of both traditional parties, ended up with a mysteriously large majority for Conservative (National Front) president-elect Misael Pastrana. This group is the one you see in Narcos taking over the Palace of Justice (which happened in 1986), stealing Bolívar's sword, and bombing the embassy of the Dominican Republic.
However, the winds of change were blowing in Colombia, and by 1986, it was clear that most people thought there must be a change in organisation from what had been seen already. Conservative president Belisario Betancur (this time, elected in non National Front elections) decided to start negotiations with the M-19 and FARC, and eventually managed for both groups to partially demobilise; the M-19 became the Alianza Democrática M-19, which set up the groundwork for the two major left-wing parties we have today, and the group of FARC members that demobilised formed a new party, the Patriotic Union. Furthermore, in 1991, the old Constitution, constructed under heavily Conservative motifs (though very heavily modified over the years) was changed through a student movement that resulted in the calling for a new National Constituyent Assembly and the drafting of a new Constitution, which is one of the most progressive ones in the world (right next to South Africa).
Of course, nobody in power liked the Patriotic Union, and with very charismatic leaders, they were seen as a real threat to the traditional two-party establishment of Colombia. One of the guys who did not like the creation of the UP was a certain Pablo Emilio Escobar Gaviria (yes, that one Colombian you all guys know) who decided that they had to go. And in traditional Escobar fashion, what ensued was the murder of thousands of UP militants between 1986 and Escobar's death. The UP was wiped out as a political organisation, FARC refused to participate in the drafting of the '91 Constitution and it seemed like the war would continue. And indeed it did, for eight of the worst years of Colombia's history as narcos reigned supreme. The President who came to power in 1994 did only through funds given to him directly by the Cali Cartel valued in the thousands of millions. The Colombian people wanted change, and elected...
...The son of the guy who stole the 1970 election, Andrés Pastrana, from the Conservative Party. Who once again decided to open negotiations with FARC and end this once and for all. This time, FARC played him like a fiddle and treated him for a fool. They stood him up at every event that he proposed, they doubled down on their terrorist attacks, kidnappings and crimes against humanity, and eventually, they were able to goad the government into granting them an area for demobilisation the size of Switzerland. Which of course, they used as a haven for kidnapping, drug smuggling and murder. It got so unsafe that between '98 and '02 three different Governors were killed, and Íngrid Betancourt, an important presidential candidate, was kidnapped.
When Pastrana's term ended the people changed courses and elected the most anti-FARC guy there was; Liberal-turned-Conservative-turned-Independent Álvaro Uribe Vélez, who promised to end the insurgency once and for all. Uribe swept to power with majorities in the first round in the 2002 election (against the most corrupt Liberal ever and Pastrana, to be fair) and soon enough set out on his promises, strengthening the ties with the US that brought us Plan Colombia, greatly increasing the military budget, and seeking a decidedly right-wing approach to law and order and the internal conflict through his motto of "Democratic Security" (which, while never losing the democratic aspect of Colombia, eventually resulted in tanks inside city slums, and near war with Venezuela). Uribe is extremely infamous for his patronage of the third major military group, the United Self-Defence Forces of Colombia (AUC), more commonly known as the paramilitaries, during his governorship of Antioquia, a policy that he continued during the Presidency (it is rumoured that he is one of the at-large para leaders). Eventually, in 2004, he brokered a deal with the paramilitary forces that mostly granted amnesty to their leading ranks and which unofficially led to a major scandal: over a third of MPs were at one point elected over paramilitary money. Those parmailitary forces that did not accept the peace deal broke away from the AUC, creating an anarchic system of Criminal Bands (Bacrim) which we haven't been able to eliminate.
Even with all his failings, Uribe did manage to lower FARC membership by over two-thirds and recover almost all of the territory of the country (when I was 2 or 3 you couldn't go from Medellín to the airport because FARC would kidnap you; now there's absolutely no problem) and cruised to direct reelection (the first in Colombian history, which required a Constitutional amendment and everything) over left-wing candidate Carlos Gaviria in 2006. When his attempts at a third term were foiled by the Constitutional Court, Uribe decided to go Putin and nominated his right-hand man; Minister of Defense Juan Manuel Santos, who had led an extremely aggressive campaign against FARC (so aggressive, in fact, that he had been accused of authorising murders against civilians) for the 2010 election. While not as successful as Uribe, he easily won in the second round against Green Antanas Mockus, and became our president.
It came as a shock to Uribe supporters nationwide when Santos began unravelling Uribe's traditional doctrine, warming up relations with Hugo Chávez and starting peace negotiations with FARC. By 2011, they had both denounced each other. Santos, however, had retained control of the major relations within Uribe's created party, the Party of the U (subtelty wasn't his strong suit) and arranged an alliance with the Liberals and populist breakaways Cambio Radical, which form our first modern political group, National Unity. On the other hand, Uribe created a new party, the Democratic Centre (officially and very ridiculously called Democratic Centre - "Firm Hand, Large Heart") which began acting as the primary opposition. And so we come to the 2014 elections...