  In this short survey we review recent results dealing with algebraic
structures (quandles, psyquandles, and singquandles) related to singular knot
theory. We first explore the singquandles counting invariant and then consider
several recent enhancements to this invariant. These enhancements include a
singquandle cocycle invariant and several polynomial invariants of singular
knots obtained from the singquandle structure. We then explore psyquandles
which can be thought of as generalizations of oriented signquandles, and review
recent developments regarding invariants of singular knots obtained from
psyquandles.
