There is quite a range of distinct styles that share this heading ~ from updated versions of the classics to all-together new and innovative styles. All are available in cordless and motorized versions along with many other options and features.
Cellular Shades
Known by many different names, these are the shades with multiple layers fused together to form air pockets and which fold up in an accordion style. It is these air pockets that make them excellent insulators which can have a big impact at very hot or cold windows. They also condense into a very compact space when they are raised to preserve complete light and view. Fabric options range from sheer, to privacy, and all the way to blackout. Cellular shades also permit you to use color in the room without detracting from the exterior of your home, as the outdoor side always has a consistent neutral appearance. There is an excellent cordless option (there are lots of shades of this type on the market with less than excellent cordless systems). There are also top down/bottom up options which can be used like a conventional shade, or can be positioned to cover only the lower portion of a window to optimize the balance between privacy and light. This is an option especially well-suited for bathrooms and bedrooms.
Roller Style Fabric & Solar Shades
The term roller shade unfortunately conjures images of the infamously cantankerous spring rollers of earlier times. These days, they most often have a continuous loop control that is easy and smooth to operate and allows you to stop them precisely at any height you wish. This is important if you have a bank of windows and you are like me in that a misaligned shade would drive you crazy. They are available in hundreds of materials from solar screens which can filter uv light while still preserving some view (perfect for sun rooms), to blackout shades for darkening bedrooms, home theaters and such. In between are all manner of fabrics in different densities, color tones, patterns and textures. One of the strong suits for these shades is that they roll up very compactly and are quite unobtrusive when they are raised. They are also well suited for doors, particularly those with lever style handles, because the fabric stays close to the door. Along with some of the other shade styles, they also have wonderful hold downs brackets available to keep shade from swishing with the movement of the door. These are magnetic and do not require bending over to latch or unlatch them from the bottom rail as so many others do. The rollers can stand alone with covers over the brackets, but most often they are concealed in a “cassette” unit covered in the same fabric, or they roll up under a small, attractive wooden valance to match or accent the room. It is a clean and straightforward look that works just as well in a contemporary setting as it does with the period house.
Natural Woven Shades
Woven of grasses and other natural materials, some of these can be fabricated to operate as roller shades, but most are made to raise and lower in folds as a roman shade. They can also hang in vertical panels that traverse left to right. At the very high end and the undisputed pinnacle, are Conrad shades. For these, the fabric goods are not rolled off and cut to size from a bolt; rather they are literally hand woven to the finished size for each window. They are gorgeous and I offer them for the occasional splurge. More often I call on another line that features beautiful designs which are based on that iconic look, but with a much more accessible price range.
Transitional Shades
versatile 
innovative 
unique beauty
Transitional shades are a relatively new style and one you really have to see to fully appreciate their unique look and function. These shades create a very striking and contemproray look that is perfect in many settings. In this category, I carry the Allure Shade by Lafayette Interior Fashions, the originator of this innovative line.
Louvered Shades
These combine some of the functionality and privacy of a louvered treatment with the less opaque fabric softness of a shade. There are essentially two layers of sheerer fabric with a more opaque fabric “louver” fused between them. This allows them not only to be raised and lowered like a shade, they can also be tilted like a blind to control light and privacy. This is a soft look that captures the elegance of a sheer with an option for more privacy and light control, all within the same shade.