A 50^th birthday is a landmark occasion. One has plenty to look back on, whilst still having much to look forward to. Plus there’s all that life experience to draw on. What’s not to feel positive about? In the case of a gallery that’s built up a remarkable reputation as an innovative space for contemporary art outside London, sheer staying power is surely to be cheered and celebrated – "hear hear" for the next 50 years, and so forth.

It took a long time for architects to embrace popular culture. I attended a talk at the Architectural Association in the mid 1970s, when someone (probably the architect Robert Venturi) waxed lyrical about shiny American diners and hot-dog stands shaped like Frankfurters and extolled the virtues of the madcap fantasies built in Las Vegas.

John Martin is heaven. Well, as many of his contemporaries would have pointed out, John Martin is also hell, or The Last Judgement, or, as the Tate’s show title would have it, the Apocalypse at the very least. For John Martin was, after Turner, the 19th century’s premier painter of catastrophe. Unlike Turner, however, he was not much rated by the more respected critics, and his work, frequently oversized, tends to spend more time in storage than on the walls of public galleries.

A beguiling shadow play greets and enchants on arrival: the silhouettes of three ballerinas, each performing an arabesque, are cast upon the wall as you enter. The effect, as their softly delineated forms dip and slowly rotate, is mesmerising. It’s also an apt opener to an exhibition devoted to exploring how Degas strove to achieve a sense of fluidity and movement in his paintings of dancers, a subject for which he is chiefly known.

A retrospective of an artist’s work is not usually a history of a working relationship, but in the case of Christo, this impressive exhibition of works from the past 40 years also marks two crucial partnerships: with his wife, Jeanne-Claude, who was his equal and co-creator from 1961, and with the Annely Juda gallery, which has mounted 12 exhibitions over four decades, as well as being intimately involved in their massive environmental “wrapped” pieces. Photographs of the end results are breathtaking, but even more gripping is watching the development of the processes over the years.

There is nothing new, nor inherently artistic, about making miniature models. Otherwise everyone who's ever stuffed a small ship into a glass bottle would be in the National Gallery. (Yes, Yinka Shonibare's fourth plinth ship-in-a-bottle outside the National Gallery is different.) But the boîtes (boxes/enclosures) of Charles Matton are of a different order entirely: recreations of artists' studios, imaginings of authors' libraries, tiny real rooms and tiny fake rooms. As well as the craft and the beauty, they challenge our very idea of seeing, space, reality.

Exhibitions with titles appended "in Britain" or "and Britain" tend to be the kiss of death: indicating concentration on a brief and insignificant visit, on the subject’s impact on British art or – even worse – the influence of local collectors on his or her reputation. With Mark Rothko, though, it has to be different. The New York abstractionist’s current near-sacred status is such that a show of his dog-ends and nail clippings would probably prove a major draw.

Hands on! Power of Making has it all: one of the most surprising and exciting collections of contemporary stuff on view for many a while. Some is functional, from coffins to bicycles, wine caskets, guns, bespoke shoes.

Every surface in my house is covered in plaster and brick dust, and wood, sand, cement, plaster and wire mesh are strewn all over the place. Furniture, carpets and pictures are covered in dust sheets and piled into two sealed rooms.

What are the most common responses to a work of contemporary art? I can think of two: “A six-year-old could have done that” (feel free to substitute “I” or “anyone”) and “But what does it actually mean?” Ryan Gander is an artist who is rather exercised by the latter. He is interested in the way we piece together scraps of evidence – overlooked details, context, history – in order to create meaning. We try to fill in the gaps. And when meaning eludes us we are often dismissive, even rather angry. Hence the protestation: “A six-year-old could have done that.” And indeed, that may well be true.