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This is an expository paper written in Spanish. This paper discusses theanswer and ideas around the Halphen question: what are the pairs (g,d) thatoccur as the genus and degree of a smooth algebraic curve in projective3-space.  Halphen's question has been studied by many authors, including Halphen in1881, Castelnuovo in 1890, and was finally answered almost 100 years later byGruson and Peskin in 1981. We (very briefly) sketch arguments by Castelnuovo instudying this question and comment on the ideas of the final answer provided byGruson and Peskin. This paper is meant to be brief and elementary introductionto some ideas about algebraic curves embedded in projective space and as such,we start out with basic definitions such as that of an algebraic curve, genusand degree. Towards the end, we mention some modern developments about thisquestion as well as directions of research.

Curvas algebraicas y la pregunta de Halphen