We can probably sort thru the vast world of cheese types by breaking them down into categorical groups from fresh to aged.  Young fresh cheeses have a high water content and a milky and delicate texture. As Cheese ages it goes thru affinage (french for refine), as the moisture in the cheese evaporates in time it leaves the fat and protein behind. This is where all the rich and savory flavor comes from in hard-aged cheeses.

Fresh and Soft Cheeses

Ricotta, Mozzarella, Burrata, Brie, Camembert,  Halloumi, Chèvre, Manchego, Mascarpone, Feta, Halloumi, Muenster, Brillat-Savarin, Crottin de Chavignol, Bûcheron

These types of cheese love crisp whites, dry rosés, sparkling wines, dry aperitif wines, and light-bodied reds with low tannins. Esp. wines with notes of apple, melon, stone fruit, tropical, berry, or citrus flavors will be perfect. Stay away from big, tannic red wines.

Wine options: Dry to Sweet Rieslings, Unoaked Chardonnays, Chenin Blanc, Gewürztraminer, Moscato, Pinot Grigio/Gris, Albariño, Grüner Veltliner, Champagne, Cava, Sauvignon Blanc, White Ports, or Fino Sherry.

Here are a few options below.

Semi-Hard, Medium-Aged Cheeses

Havarti, Edam, young Cheddar, Monterey Jack, Emmental, Gruyère, Jarlsberg, Manchego, Tomme d'Alsace

Medium-bodied whites, vintage sparkling wine, fruity-reds and wine based aperitif will be perfect matches. With these cheeses being more firm in texture and stronger in flavor these wines below will offer a balance between acidity, fruit, and tannins.

Wine options: Chardonnay, Viognier, white Burgundy, white Bordeaux, Pinot Blanc, white Rhône blends, Riesling (off-dry), Gewürztraminer, Champagne, red Burgundy, Pinot Noir, Beaujolais, Dolcetto, Barbera, Zinfandel, Merlot, vintage Port, young Tawny Port, Amontillado sherry

Here are a few options below.

Washed Rine - Stinky Cheeses

Camembert, Epoisses de Bourgogne, Livarot Munster, Taleggio, Limburger

These powerfully aromatic cheeses require wines that are light-bodied with modest aromatics that complement not compete with these smelly cheeses.

What works best with these are Gewürztraminer, Riesling, red Burgundy, Pinot Noir and Sauternes.

Here are some great examples below.

Blue Cheeses

Gorgonzola, Stilton, Roquefort, Cambozola, Bleu d'Auvergne

These cheeses desire wines with both power and sweetness to balance their bold flavors and usually very salty, savory flavor.

Wines like Ruby Port, Tawny Port, Banyuls, Sauternes, Oloroso sherry, Tokaji, or Recioto, 

Hard-Aged Cheeses

Aged Cheddar, Cheshire, Comté, aged Gruyère, aged Gouda, Pecorino, aged Manchego, Asiago, Parmigiano Reggiano

These cheeses are made for full-bodied whites and tannic reds. The nuttiness works great with sherry and saltiness makes them perfect matches with sweeter wines.

Pair with wines like Burgundy-white or red, Bordeaux-white or red, Rhone-white or red, sweet Riesling, Viognier, vintage Champagne, Cabernet Sauvignon, Petite Sirah, Barolo, Barbaresco, Nebbiolo, California red blends, Zinfandel, Ruby Port, Tawny Port, Madeira, Sauternes, Oloroso sherry.