Clean the seafood: scrub mussels and clams, remove beards; peel and devein shrimp; cut squid into rings. Discard any open shellfish that don't close when tapped.
Bring a large pot of salted water to a boil. Cook pasta until al dente, about 1 minute less than package directions. Reserve 1 cup pasta water, then drain.
While pasta cooks, heat olive oil in a large skillet over medium heat. Add garlic and red pepper flakes; cook until fragrant, about 1 minute.
Add the white wine and let simmer for 2 minutes to reduce slightly.
Stir in crushed tomatoes and tomato paste. Season with salt and pepper. Simmer for 10 minutes, stirring occasionally.
Add the mussels and clams to the sauce, cover, and cook for 3-4 minutes until they start to open. Add shrimp and squid; cook for another 2-3 minutes until shrimp are pink and squid is opaque. Discard any unopened shellfish.
Toss the cooked pasta with the seafood sauce, adding a splash of reserved pasta water if needed to loosen. Sprinkle with parsley and serve immediately.
Tips
Use a mix of your favorite seafood; mussels and clams add briny flavor.