Surveys of Current (last 50 years) Mathematics at Graduate / Research level?

Question

What books or broad survey articles survey the mathematics of the last 50-100 years?

The ones I've read do a good job conveying mathematics from the ground up but typically assume a complete beginner or high school student audience and therefore reach only as far as the advanced undergraduate curriculum (middle of the 19th century).

I'm looking for something to pick up the thread from here, starting in the mid-1800s, and continuing through the 1930s and 40s, to the present. I'd like to see solid survey coverage, in the same accessible style, of 20th century mathematics: algebraic or differential topology, PDEs, algebraic geometry, number theory, calculus of variations, optimisation, analysis, abstract algebra, galois theory, functional analysis, etc.

It would be ideal if the intended audience were presumed to have an undergraduate degree in mathematics or even a graduate degree. Even better if the audience were presumed to include mathematicians specialising in one particular area but interested in the breadth of the field, or if the intent were to familiarize a technically specialized audience of statisticians, computer scientists, engineers, or physicists, with the breadth and directions of current active areas of investigation and research in mathematics.

Any particularly well-written such books & articles you have come across?

Examples of Surveys of the first kind (not modern):

• Kolmogorov, et.al., Mathematics: Contents, Methods & Meaning,
• Gellert, et.al., VNR Encyclopaedia of Mathematics
• FeliKlein's (Advanced Mathematics from an Elementary Point of View).

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Edit (July 2016):

The Princeton Companion to Mathematics (ed. Timothy Gowers) came out in 2008 and turns out is probably the best possible such reference, see the accepted answer.

Super excited to see that in 2015, we now also have the Princeton Companion to Applied Mathematics (ed. Nicholas Higham), which covers the modern aspects of applied and applicable mathematics in the same format as Gowers' masterpiece!

Answer 1

A fairly comprehensive survey is given in the Princeton Companion to Mathematics, edited by Timothy Gowers. The book contains a lot of material by many great mathematicians. In terms of the level, early undergraduates can benefit from the book, but probably everyone could learn something new. The only downside is that it is really, really heavy.

Answer 2

These are the ones I had come across before posing the question. Though none of them were quite what I was after (see accepted answer of Princeton Companion to Mathematics), they're recorded here in case they are useful to others:

• Modern Mathematics in the Light of the Fields Medals, by Michael Monastyrsky

• What's Happening in the Mathematical Sciences, yearly 200x-200x+1 de Barry Cipra, so far 9 volumes.

• This MathOverflow list is a great selection of books with an historical perspective on various areas of modern mathematic

• A Panorama of Pure Mathematics (Pure and Applied Mathematics (Academic Pr) by Jean A. Dieudonne, although this has not received many favourable reviews.

• Encyclopaedia of Mathematical Sciences, V.I. Arnold (editor-in-chief), although this is a series consisting of some 160 and counting hardback books, most written by leading Russian mathematicians. Besides the sheer number of volumes and hence page count, each is typically upwards of $100, so significantly less accessible in price as well...

• Encyclopaedia of Mathematics, Springer & the European Mathematical Society, an online collection of articles on mathematical topcs.