The story so far...

Aaron Hotchner and Emily Prentiss met long before Emily joined the BAU. In her first appearance in Criminal Minds, in 2x09 'The Last Word,' we discover that one of Hotch's earliest assignments as a new Agent was to work security detail for Emily's mother, Ambassador Prentiss. About that time, Hotch believed that Emily was heading to Brown, an Ivy League University in the Northeast. She informs him, when they meet again, that she actually went to Yale, and had been working in the Midwest since joining the Bureau.

The Agents' first meeting after an almost ten-year interlude is somewhat tense, and Hotch immediately suspects that Emily used her political and family connections to transfer to his Unit. Hotch was given no notification that she was about to join, it seems, in place of Elle Greenaway, who had recently left in less than happy circumstances. 

A few days after their first meeting in Hotch's office, Hotch arrives back from a case to find Emily waiting for him. Her acceptance into the BAU must be approved by Hotch. She is persistent, and impresses him with her approach to a case the team is working on. He grudgingly accepts that she is now at least provisionally part of the team, and tells her to get herself set up with a desk the next morning, and when to attend team briefings. The episode ends with Emily telling Hotch he won't regret it.

Emily's first few months in the BAU are difficult, as she strives to build professional relationships with the already tight-knit team. Although he remains the consummate professional, Hotch's hostility towards her grows, alongside his suspicions. 

A 'break' in the tension comes in 2x11, 'Sex, Birth, Death'. Hotch is convinced that Emily is consorting with a local politician who insists that Hotch keep the news of a series of murders of prositutes quiet. He is cold towards Emily, then finally confronts her:

Hotch: 'You mysteriously showed up at the BAU after one of my team members was involved in a questionable shooting.'

Emily: (whipsers) 'Right.'

Hotch: 'You've done good work, I'm not questioning that. But I will not put up with a political agenda.'

Emily: 'My mother's a career politician - you worked with her...did you like her?'

Hotch: 'She's an impressive woman.'

Emily: 'Well...I think politics makes people distrustful. I think it makes them hate themselves. I think it tears families apart, and damages people.'

Following this encounter, Hotch comes to trust Emily a little more, clearly coming to doubt his previous perceptions. 

In 2x14, 'The Big Game', the team and Haley Hotchner are together in a bar, on a rare night out, when Haley asks Emily how they're  treating her at the BAU. Hotch cuts in and clarifies: 'she means am I being nice to you.'

At the beginning of season 3, Hotch is temporarily suspended by Section Chief Erin Strauss, for questionable conduct on a case in which a girl committed suicide and killed the unsub. Strauss takes control of the team, and airs her belief that they would be better off without Hotch or Gideon's leadership. While Hotch is at home, suspended, Haley suggests that he look for an alternative role in the FBI - one that will give him more time with his family. This notion is supported by Strauss. Hotch comes to the Bureau to discuss this with Strauss, and their meeting is interrpted by Prentiss, who informs Hotch that she is quitting the FBI and hoping to take the Foreign Office exams. Hotch tells her he thinks this is a mistake, but she is firm in her decision. The team travels to Milwaukee, minus Hotch and Prentiss. Morgan frequently contacts Hotch for advice, until he can take it no longer, and packs a bag to go join them, to help out for 'one last case'. Haley gives him an ultimatum: his family or his team. He leaves, assuring her that he will return soon. He heads straight for Prentiss's apartment, where he finds her defensive and unwilling to talk. He asks her to come with him to Milwaukee, despite the fact that neither have badges, guns, or any real authority. It is revealed that Strauss had been attempting to use Prentiss to unearth information on Hotch and the team, to hamper their progress and Hotch's ambitions of rising through the FBI's ranks. Prentiss refused, and chose to quit the BAU, rather than betray Hotch. They talk about this, and Prentiss agrees to join him in Milwaukee, where both resolve to re-join the BAU.

Thereafter, Hotch and Prentiss are frequently teamed up in season 3, and they often appear to complement one another, almost knowing what the other is thinking.

They gain further insights into, and understanding of, each other's characters.

For example, in 3x04, 'Children of the Dark', Prentiss's maternal side emerges when she wants to take an orphaned girl back to DC with her. Hotch reminds her that 'this is the job, and I need to know you can be objective.' Without missing a beat, Emily replies: 'I need to know I can be human'.

By season 4, the Agents appear to have reached an understanding that could be viewed as a friendship of sorts. Hotch frequently asks for her opinion, and often takes her advice to heart. In 4x09 '52 Pickup', she tells him in not so many words, to go easy on JJ's temporary replacement, Jordan Todd. Emily reminds Hotch that she was once the new team member, and knows how it feels. At the end of the episode, Hotch commends Jordan for her work, mentioning Emily had put in a good word for her.

There are many examples of their burgeoning relationship in season 4 - see the 'episodes' section.

Season 5 begins with Hotch gone AWOL, and Emily feeling concerned enough to break away from the rest of the team and go to his apartment, only to find evidence of a struggle having taken place - but Hotch is nowhere to be found. Garcia finally tracks him down to St Sebastian's hospital where he was left by The Reaper, a.k.a. George Foyet. Emily is upset  and extremely concerned when she finally sees Hotch, and keeps vigil by his bedside until the rest of the team arrives at the hospital. 

In the first few episodes of season 5, Emily quietly and discreetly looks out for Hotch's well-being - driving him to and from work when he returns from his leave of absence, and keeping close to him as they work on new cases. 

Many Hotch/Prentiss fans, or 'shippers' know that the chances of a romance developing between characters on Criminal Minds are slim. However, they still enjoy 'reading between the lines' while watching CM episodes, and creating fan fiction, art, videos, and other tributes to what they consider to be a good romantic pairing.  The romance is just for fun, and most of us truly enjoy the friendship, trust, and understanding that has grown between Hotch and Prentiss over the past few years. The actors who portray Prentiss and Hotch, Paget Brewster and Thomas Gibson, have fantastic onscreen chemistry, which is a joy to watch.

Long may it continue!