This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), physics, engineering, economics, medicine, biology, psychology, ecology, etc.

Rational curves are subdivided according to the degree of the polynomial.

Plane curves of degree 2 are known as conics or conic sections and include

Cubic plane curves include

- Cubic parabola
- Folium of Descartes
- Cissoid of Diocles
- Conchoid of de Sluze
- Right strophoid
- Semicubical parabola
- Serpentine curve
- Trident curve
- Trisectrix of Maclaurin
- Tschirnhausen cubic
- Witch of Agnesi

Quartic plane curves include

- Ampersand curve
- Bean curve
- Bicorn
- Bow curve
- Bullet-nose curve
- Cartesian oval
- Conchoid of Dürer
- Cruciform curve
- Deltoid curve
- Devil's curve
- Hippopede
- Kampyle of Eudoxus
- Kappa curve
- Lemniscate
- Limaçon
- Ovals of Cassini
- Squircle
- Three-leaved clover

- Astroid
- Atriphtaloid
- Nephroid
- Quadrifolium

- Epicycloid
- Epispiral
- Epitrochoid
- Hypocycloid
- Lissajous curve
- Poinsot's spirals
- Rational normal curve
- Rose curve

- Bolza surface (genus 2)
- Klein quartic (genus 3)
- Bring's curve (genus 4)
- Macbeath surface (genus 7)
- Butterfly curve (algebraic) (genus 7)

- Polynomial lemniscate
- Fermat curve
- Sinusoidal spiral
- Superellipse
- Hurwitz surface
- Elkies trinomial curves
- Hyperelliptic curve
- Classical modular curve
- Cassini oval

- Bowditch curve
- Brachistochrone
- Butterfly curve (transcendental)
- Catenary
- Clélies
- Cochleoid
- Cycloid
- Horopter
- Isochrone
*Isochrone of Huygens*(Tautochrone)- Isochrone of Leibniz[1]
- Isochrone of Varignon[2]

- Lamé curve
- Pursuit curve
- Rhumb line
- Sinusoid
- Spirals
- Syntractrix
- Tractrix
- Trochoid

- Blancmange curve
- De Rham curve
- Dragon curve
- Koch curve
- Lévy C curve
- Sierpiński curve
- Space-filling curve (
*Peano curve*)

See also List of fractals by Hausdorff dimension.

- Conchospiral
- Helix
- Hemihelix, a quasi-helical shape characterized by multiple tendril perversions
- Tendril perversion (a transition between back-to-back helices)

- Seiffert's spiral [4]
- Slinky spiral [5]
- Space cardioid
- Twisted cubic
- Viviani's curve

- Caustic including Catacaustic and Diacaustic
- Cissoid
- Conchoid
- Evolute
- Glissette
- Inverse curve
- Involute
- Isoptic including Orthoptic
- Negative pedal curve
- Orthotomic
- Parallel curve
- Pedal curve
- Radial curve
- Roulette
- Strophoid