The cosmic century
Longair packs an lot of material into the 450 pages of the book, and the history continues up to 2006, and so I felt that it gives a fairly comprehensive overview of current research into cosmology and astrophysics, but without being too technical. There is a bit of maths in the text, but it isn't intrusive (many of the chapters have an appendix with a mathematical derivation of a significant result). Readers do need some prior knowledge of the subject but I would think most science undergraduates would have no problems following the book. Certainly if are thinking of doing research in these subjects, or if you want a substantial overview of the field then I would say that this book deserves a place on your bookshelf.