In early 1660, was there truly a bunch of monkeys in the Dutch House? He says he got home another day from a short trip and the monkey was loose so he struck it - what does this mean?
This is the mention from that day (I'll reproduce the full day's entry below, for context -- it's short).
At home found all well, but the monkey loose, which did anger me, and so I did strike her till she was almost dead, that they might make her fast again, which did still trouble me more.
He's most likely talking about a Barbary macaque, Macaca sylvanus, which live mostly in the Atlas mountains of northwest Africa and also (in small numbers) in Gibraltar, having been introduced there at some point (arguments on when differ, but before 1704, when the British took control of the peninsula).
Pepys collected odd and interesting things, like many people of his station did at the time, and has a few references in his diaries of visiting monkeys at friends' homes, watching monkeys (plural) dance, and so forth. Interestingly, he records taking his wife to watch monkeys dance three times at Bartholomew Fair, on Aug. 31, 1661, and Sept. 4 and 7, 1663, although he's not totally a fan of it at any time. These are very offhand entries, not as though he's seeing some massive natural wonder, which leads one to think that these are curiosities, not once-in-a-lifetime events.
There are also references to "ape[s]" both literally (Feb. 7, 1661/62) and metaphorically (Nov. 22, 1666). These are separate from the "great baboon" he references from "Guiny" (modern-day Ivory Coast/Senegal, generally) that Capt. Robert Holmes had brought back from his (in)famous expedition of 1664, which arguably started the second Anglo-Dutch war. Of this animal he says:
At the office all the morning and did business; by and by we are called to Sir W. Batten’s to see the strange creature that Captain Holmes hath brought with him from Guiny; it is a great baboon, but so much like a man in most things, that though they say there is a species of them, yet I cannot believe but that it is a monster got of a man and she-baboon. I do believe that it already understands much English, and I am of the mind it might be taught to speak or make signs.
So ... it's not clear what kind of a beast that was. Like a lot of people, Pepys was imprecise with his descriptions (quick, without googling, what's the difference between a monkey and an ape, and which of those has a subset we call humans?), but it's not at all unusual that in an age of exploration that people who fancied themselves natural philosophers would either attempt to own, or have access to, all sorts of creatures from the places the English navy was exploring.
The original monkey entry is below, from Jan. 18, 1660/61:
The Captains went with me to the post-house about 9 o’clock, and after a morning draft I took horse and guide for London; and through some rain, and a great wind in my face, I got to London at eleven o’clock. At home found all well, but the monkey loose, which did anger me, and so I did strike her till she was almost dead, that they might make her fast again, which did still trouble me more. In the afternoon we met at the office and sat till night, and then I to see my father who I found well, and took him to Standing’s to drink a cup of ale. He told me my aunt at Brampton is yet alive and my mother well there. In comes Will Joyce to us drunk, and in a talking vapouring humour of his state, and I know not what, which did vex me cruelly. After him Mr. Hollier had learned at my father’s that I was here (where I had appointed to meet him) and so he did give me some things to take for prevention. Will Joyce not letting us talk as I would I left my father and him and took Mr. Hollier to the Greyhound, where he did advise me above all things, both as to the stone and the decay of my memory (of which I now complain to him), to avoid drinking often, which I am resolved, if I can, to leave off.
Hence home, and took home with me from the bookseller’s Ogilby’s Aesop, which he had bound for me, and indeed I am very much pleased with the book.
Home and to bed.
It's probably also worth pointing out that here, the context is Pepys traveling back to his house after spending a couple of days looking after the welfare of Jemima Montagu, the countess of Sandwich (that is, the wife of the Earl of Sandwich^1, Pepys' patron), and after his wife had been out of the house earlier that week, sitting with a sick friend. The air of the week's entries is that he's rather displeased with his wife, and the monkey may well have been made to suffer for it. But Pepys is an unreliable narrator at best, so we can't be totally sure.