<p>Various lines of evidence are pointing to the possibility that the dynamo mechanism powering the solar magnetic activity cycle may be operating very close to, or even below, criticality. Such evidence includes the sudden drop in angular momentum loss in magnetized winds inferred in solar-type stars slighty older than the sun, and the ability of dynamos operating at or very close to criticality to generate solar-like patterns of long-term amplitude modulation when subjected to (relatively) weak stochastic forcing. After reviewing the notions of subcriticality, criticality and supercriticality in the context of the classical mean-field <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mi mathvariant="normal">Ω</mi> </mrow> </math></EquationSource> </InlineEquation> dynamo model, I review the broader extant literature on the topic and present a simple model based on energetics that provides upper bounds on the finite amplitude sustained by an otherwise subcritical large-scale “primary” dynamo in the presence of a secondary dynamo process. This allows new scenarios for intermittency, which are presented and discussed in qualitative terms, together with implications for our understanding of long-term solar cycle variability.</p>