Byakuya Kuchiki is absolutely stunning, with long raven hair, porcelain white skin, slim athletic yet muscular physique and chiseled yet delicate, fine features. The topper is his eyes: a smoldering grayish/violet which can turn an icy grey or a blinding violet depending on his mood.
He's incredibly strong, has immaculate manners, and appears icy. Byakuya has a huge heart which has suffered much throughout his life. He was used by his parents for his abilities. The ways of nobility were literally beaten into him by teachers, etc. Yet, somehow, he managed to not let his spirit die. With the death of his parents, he was freed. Then 50 years ago, he married and broke every law/rule/etiquette of society there was to marry Hisana. He had truly loved Hisana and had for the first time felt complete. He had so many hopes and dreams about a life together with her. They had five wonderful years together and then she died and his heart shattered . . . since then, no one had truly attracted Byakuya and he could not forget his beautiful wife.
The Rukia came into his life. He handled that all wrong but, it was difficult for him to show affection, afraid if he got too close, formed a bond, it would be taken away from him. But after the devastation with Aizen's betrayal and Rukia's near execution, he had learned his lesson, the hard way. He began to open up to Rukia and began to see she was someone whom to shower with his caring and love. She was not just his sister-in-law, but his sister. He'd never had siblings; it was nice to have to take care of someone in a way not related to his duties as captain. He finally had family again.
And there was also Yachiru with whom he somehow managed to develop an amusing relationship with. He'd grown to care deeply for the young Lieutenant. And unbeknownst to him, Yachiru utterly adored and loved her Byakuchi-chan.
He of course had working relationships with the other captains, etc. The one he clashes with most often is Zaraki and that's b/c Zaraki always argue with him, insult him, they get into verbal sparring, etc. Zaraki simply drives B nuts though he hides it perfectly unlike Zaraki who just insults him and walks away. The clashes between the two provided some of the best entertainment in Seretai with their disputes, insane bets and B's idea of diplomatic relations.
The 13 Squad subordinates and most seats fear and respect Byakuya.
A plot is in the works and steps are beginning to be carried out to capture Byakuya Kuchiki. His powerful reitsu is the reason for this plot, desire for him is the ulterior motive. What happens from here on out will reveal test Byakuya's strength like nothing in the past and his hidden powers, those of his childhood which he has suppressed for years will be revealed.