When people talk about playing companies around Shakespeare's day, they mostly talk about the company Shakespeare acted with (called first The Lord Chamberlain's Men, and after James was crowned, The King's Men), and The Admiral's Men performing in The Rose theatre. However there were several other companies in London, including The Lord Strange's Men and The Pembroke's Men. Where there is not a great deal known about this company, we do know that they had several very financially successful tours, and that they got in a lot of trouble over a play called The Isle of Dogs. This play caused enough of a stir with its political satire that three of the Pembroke actors were arrested.
Last week I wrote about title pages, and one of the things we know from the title page of The Taming of A Shrew is that The Pembroke's Men performed it. When it was published in 1594, it was likely published by the company, although we cannot know for sure. For more about The Lord Pembroke's Men, see the information on the Lost Plays database. The following timeline shows key points from their information on the right, and contemporary events in London on the left.
Again, thanks for reading and feel free to comment with questions if there are things you'd like to hear about!