Cerulean, meaning “sky”, is a light-valued earth blue on the cyan side, traditionally made from the PB35 or PB36 pigments, which are both cobalt oxides. It is opaque and granulating.
Warning: Be careful to look at pigment numbers. Some brands, like Mission Gold, call their PB15 Phthalo Blue “Cerulean.” Don’t make the mistake I did when I first started painting, and get “Cerulean Hue” (from Da Vinci, Cotman, etc.), made from Phthalo Blue + white. PB15 is not the same color, and will not have the same granulation/magic/mixing properties.
Experiment Results

Gradient: A highly granulating gradient between a middle green-blue, to a pale sky blue. Doesn’t get very dark.
Opacity: Semi-opaque. This is the most opaque color in my palette (and it’s still not THAT opaque).
Glazing: Glazes to medium cornflower blue.
Lifting: Back when I only knew about wet-paint lifting, I didn’t really understand why Cerulean was considered an especially liftable paint. If anything, it lifts less cleanly than a Phthalo and makes less realistic cloud shapes. But when you do a dry-paint lift (scrubbing with a wet paper towel on dried paint), WOW, I See It. It’s like erasing a pencil mark, quick, easy, and gets completely white as if I never painted there at all!
Lightfastness Test
I tested Da Vinci Cerulean Blue Genuine.

After six month of light exposure, the left (exposed) swatch is infinitesimally warmer (more violet-toned/less green-toned) than the protected swatch, noticeable only in tints. It’s extremely hard to tell. I would generally give this an A grade.
Comparison to Other Brands
Daniel Smith – Cerulean Blue Chromium

Daniel Smith offers a Cerulean (similar to Da Vinci’s offering) as well as a darker, greener, more granulating Cerulean Blue Chromium.

I find the CBC is more interesting as a mixer but less suitable to skies.

Color Mixes
I found the color mixes for Cerulean to be surprising and lovely!
Lemon Yellow (PY175)

Hansa Yellow Medium (PY97)
Range of granulating teals, mints, and yellow-greens. I especially like the cool mint foliage color (similar to Cobalt Green). I found it difficult to keep the lemon from overwhelming the blue.

Monte Amiata Natural Sienna (PBr7)

I was expecting either green or gray and didn’t get either – it’s staunchly simultaneously tan and blue! The balanced mix, with its granulation that looks like reflected light, gives me the impression of looking through clear water to the sandy bottom of the pond.
Transparent Red Oxide (PR101)

Love the clean brown and the medium brownish-tannish-blueish grays, perfect for rocks. A tiny touch of TRO in mostly blue gives a nice gray cloudy cast to the sky color.
Naphthol Scarlet

You can make an interesting Perylene Violet -ish hue from this combo, or soft gray-violets that look good in clouds.
Deep Scarlet (PR175)

Nearly complementary, though a bit on the purple side; resulting in a range of soft violet grays, brick reds and slate blues. More muted than the Napthol Scarlet mix.
Perylene Maroon (PR179)

Very similar to Deep Scarlet mixes.
Indian Red (PR101)

This is one of the most even/neutral gray mixes I have found. I really like the lovely gray that can be made here, which turns either toward a violet-brown or a slate blue depending on the balance. I like these earthy granulating grays for mountains and rocks. It is ideal for a mid-value gray, as it doesn’t get dark/black like the Ultramarine + Transparent Red Oxide mix.
Potter’s Pink (PR233)

A super-separated, granulating purple-cloud sky mix.
Perylene Violet

This is also a moody, cloudy-sky mix.
Perylene Red (PR178)

Moving in a slightly cooler direction with reds, this crimson gives us muted mauve / violet mixes, which are still on the grayish side.
Pyrrol Rubin (PR264)

We edge incrementally cooler! We’re getting more violety hues now, and I especially like the grayed blue which I think looks very cloudlike. I like these better than the PR178 mixes.
Permanent Alizarin Crimson (PV19, PBr25)

Made from a mix of Quin Rose and Imidazolone Brown, Holbein’s Permanent Alizarin looks similar to PR264 unmixed but mixed much more violet and vivid mixes. Still, these are not so bright that you couldn’t use them for clouds. I feel like the balance mix looks like Ultramarine Violet.
Quin Red (PV19)

Quin Coral (PR209)

Slightly more muted than the Permanent Alizarin Crimson mixes, but still fairly vivid, and making a nice Lavender hue in dilute.
Quinacridone Magenta (PR202)

Fairly vivid lavender/violet mixes, with some depth to them from the deeper magenta.
Quin Violet (PV19b)

Moving more violet still, these mixes are similar to PR202’s but a bit more straightforwardly purpley. I kinda like PR202’s interesting mixes better.
Cobalt Violet (PV14)

This very granulating violet meets very granulating CBG to mix very granulating, color separating, pastel violet mixes.
Indanthrone Blue (PB60)

Sort of Ultramarine and Cobalt hues, a little lower chroma, and also kind of pointless since Ultramarine Blue is easier and cheaper to get than Cerulean and this specific Indanthrone.
Phthalo Green Blue Shade (PG7)

Bright, pretty turquoises and sky blues with cerulean granulation floating over the green.
Serpentine (Primatek)

There’s something so interesting about these greens and blues that don’t quite ever mix. It’s turquoise but a much duller shade than, say, Cobalt Turquoise. If I’m being uncharitable it looks like pond scum.
Terra Cotta (PR102)

Venetian Red (PR101)

Indian Red (PR101)

What Others Say
There are a number of other blue and turquoise blues made from PB36. I like this one [Daniel Smith Cerulean Blue Chromium], mixed with Ultramarine, for blue skies anywhere in the world. It is granulating and liftable, which is very important when doing skies so you can lift out the clouds.
Jane Blundell, Cool Blues
Cerulean Blue has a greener bias than that of Cobalt Blue or Ultramarine Blue. It also granulates and has slightly chalky characteristics. It is useful for skies – particularly in winter, as its relative coolness indicates cooler conditions.
David Webb, Watercolor: The Indispensible Guide (2016), p. 35
I actually disagree with the above as I think that “warmer” (i.e. more violet-toned) skies look more wintry, because in my experience the air is dry and clean in winter and you can see the “true” violet-toned color of the sky better. The green bias and dinginess of Cerulean to me looks more like the sky in summer, when it tends to be more humid and smoggy. But the relative humidity in different seasons varies from place to place.
I also don’t think that Cerulean is “chalky,” at least not compared to hues mixed with white.
Cerulean is lovely for winter skies, providing a nice cool touch to the horizon. It creates delicate foliage greens, gorgeous rock pools, rivers, lakes. Beautifully cool and refreshing. The textural effects it gives makes it a great choice for soil, foreground, bark.
Debi Riley, Dive Into the Mysteries of Blue (2015)
The cobalt cerulean and turquoise pigments are a definite preference among some artists, who rely on them to temper warm mixtures and create subtly textured pale blue washes (cerulean skies really are unique). … Cerulean blue is an excellent palette complement to ultramarine blue.
SUBSTITUTIONS. All the cobalt cerulean/turquoise paints are relatively dull, and therefore are fairly easy to approximate with a mixture of cobalt blue with cobalt teal blue (PG50), or ultramarine blue with phthalocyanine green BS (PG7).
Bruce MacEvoy, handprint.com (2010)
My Overall Review
I have to say Cerulean Blue is one of the most popular pigments that I didn’t understand – at least, not at first. Everyone always talks about it as a sky color, but I don’t find the hue to be particularly sky-like, at least, certainly not more so than a mix of Ultramarine and Phthalo Blues. You can lift it, but I don’t do a lot of lifting – I’d rather paint around clouds. Granulating skies can be pretty, and can approximate certain types of tiny “mackerel” clouds, but for the most part I don’t usually prefer granulating skies. I think the sky looks smooth in real life.

I think Cerulean Blue is usually more gratifying to me when used as a cloud color, rather than base sky color.

But skies aren’t the only thing to do with Cerulean Blue. Don’t sleep on it as a granulating mixer that goes great with earth red or maroon to make soft grays.

Favorite Version: Da Vinci Cerulean Blue Genuine, by far. I find it the most useful as I like its bright skies as well as its gently granulating mixes. DS Cerulean Blue Chromium is an interesting “special effects” paint when you want a ton of granulation in your mix, but it doubles down on the things I dislike about Cerulean Blue, i.e. being weak, muted and greenish.
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Da Vinci – Cerulean Blue Genuine, 8ml tube: Da Vinci Paints
Da Vinci – Cerulean Blue Genuine, 15ml tube: Da Vinci Paints | Blick | Utrecht