Love was an emotion which K9 Mark 2 struggled to understand, receiving no clear answer when asking his human company. (TV: Aeolian) Peri Brown defined it to Yrcanos, the man who would become her husband, (TV: The Ultimate Foe) as "when you care for someone or something more than yourself", "sometimes more than life." (TV: Mindwarp)
In his youth, the First Doctor authored a treatise on the chromosomal origins of love for which he received a "rubbish" grade with his tutor stating he'd missed the point entirely. (AUDIO: The Wormery) At the end of his life, the First Doctor noted love as an example of emotions to the Cyberman leader Krail, along with hate, pride and fear. He questioned, "Have you no emotions, sir?" (TV: The Tenth Planet, Twice Upon a Time) His twelfth incarnation later declared that love was not an emotion but a promise. (TV: Death in Heaven)
Although River Song once declared her belief that the Doctor was above the capacity for romance, (TV: The Husbands of River Song) they proved themselves capable, on occasion, of expressing romantic feelings for others.
When with the Aztecs, the First Doctor accidentally got engaged to a woman called Cameca, when she poured cocoa beans in front of him, not realising the Aztec symbolism that sharing cocoa was a proposal of marriage. Cameca gave him a brooch during his visit, which he was planning to leave behind before leaving in the TARDIS, but then picked up again, indicating that he did show real affection for Cameca. (TV: The Aztecs)
The Sixth Doctor once confessed that be believed he was falling in love with Bianca, an evil future incarnation of Iris Wildthyme, though these feelings were ultimately a ploy by the Doctor to defeat her, as well as an effect of the psychic worms in the alcohol Bianca had given the Doctor. (TV: The Wormery)
On his regeneration into his eighth incarnation, the Doctor began to explore the realms of romantic connections with others, quickly sharing a kiss with Grace Holloway. (TV: Doctor Who) After travelling with the Eighth Doctor for several weeks, Charley Pollard realised that she'd fallen in love with him. (AUDIO: Letting Go) She confessed these feelings to the Doctor when she felt she was going to die, (AUDIO: Neverland) and the Doctor confessed that he loved her as well, but their relationship remained platonic. (AUDIO: Scherzo)
The Tenth Doctor had a number of female admirers, including Queen Elizabeth I, to whom he got married and left behind at the altar. (TV: The Day of the Doctor) He once fell in love with Madame de Pompadour, who took him away to "dance". He was particularly saddened by her death before she had the opportunity to travel with him. (TV: The Girl in the Fireplace) Rose was openly jealous of the Doctor's relationships with both Madame de Pompadour and Sarah Jane Smith. (TV: School Reunion) When saying goodbye to the Doctor, Rose admitted that she loved him, a feeling that the Doctor was unable to voice a reciprocation for. (TV: Doomsday, Journey's End)