Double degraders and uses thereof

A compound of formula I-IV:

• or a pharmaceutically acceptable salt thereof, wherein:
• LBM is a E3 ubiquitin ligase binding moiety;
• IBM is an IRAK binding moiety capable of binding to one or more of IRAK1, IRAK2, IRAK3, IRAK4, preferably IRAK4;
• BBM is an BTK binding moiety capable of binding to BTK;
• La is a bivalent moiety that connects LBM to IBM;
• Lb is a bivalent moiety that connects LBM to BBM;
• Lc is a bivalent moiety that connects IBM to BBM;
• Lx is a bivalent moiety that connects LBM to X;
• Ly is a bivalent moiety that connects IBM to X;
• Lz is a bivalent moiety that connects BBM to X;
• and
• X is a trivalent moiety that connects Lx, Ly, and Lz.