A very recent programme is the "transcendental syntax" promoted by Girard, the founder of linear logic, since 2011. As the Kantian name suggests, the idea is to develop a "critique of grammar", intrinsic justification of logical rules that we adopt as conditions of possibility, similar to Kant's justification of the "synthetic a priori". Obviously, logical justifications for logic would be circular, and semantic (empirical) justifications run into well known epistemological problems. The idea is to reinterpret deductions as dynamically executed programs along the lines of Curry-Howard correspondence, introduce tests for and against assertions, and interpret the rules as ensuring successful termination of disputes about them. This partly models the normative practice of logic, which Wittgenstein thought "must be passed over in silence" wholesale. In Girard's words, "transcendental syntax substitutes for the semantics - i.e., the metaphysics of "Real" - the study of the conditions of possibility of logical language", as successfully executable.
Here is Girard's programmatic paper, but I'd start with the more expository On Trascendental syntax: a Kantian program for logic? by Abrusci and Pistone, which puts it into historical context:
"In analogy with Kant’s transcendentalism, indeed, the program tries to raise the issue to deduct, that is, to legitimize the authority exercised by logical languages... without reference to those entities whose representability crucially relies on the use of what is charged of being justified; this constraint was indeed the one making a difference, for Kant, between the transcendental enterprise and metaphysics.
[...] aims at an explanation of how syntactical constraints are related to traditional logical results such as general cut-elimination theorems, completeness and incompleteness theorems. [...] at least two other ambitions: the use of transcendental syntax tools to exert a critical power towards existing syntaxes, by putting together philosophical justifications and purely technical ones and the refinement of actual logical systems, along with a finer understanding of their inner constitutive principles."
Also take a look at the recent volume Logic, Epistemology, and the Unity of Science (2009) edited by Rahman et al. It is a thematic collection of papers centered on the role of logic in analytic philosophy. It reflects a recent movement with the ambition to philosophically revive some aspects of logical positivism (unification of knowledge on the basis of logic), but on Neurath's "encyclopedic" conception rather than Carnap's "elimination of metaphysics through syntax" one. Here is from the programmatic opening article:
"While many philosophers of science have shied away from logic there have, in the meantime, been many important new developments in logic, some of which may have extremely significant applications to questions in epistemology and general philosophy of science. These developments have gone virtually unnoticed in the broader philosophical community. One of the purposes of this volume is to encourage philosophers to recognize the potential riches to be found in recent work in logic, for instance in the plethora of non-classical logics, including, prominently, game theoretical semantics and independence-friendly logic...
Distancing ourselves from scientism does not mean separating ourselves from
the project of the Vienna Circle. Quite the opposite. We reject the easy caricatures that too often pass for history with respect to these philosophers and insist instead on emphasizing the progressive, collaborative and optimistic spirit of their Encyclopedia project... Neurath’s boat, like the scientific project itself, is an improvised assembly of components, adjusted on the fly and always subject to reconstruction. Nevertheless, as long as the sailors survive, they find their community engaged in a single unified project."
See also an earlier question What are the major research programmes in contemporary logic?