In this extended abstract, we present approximation algorithms for the following packing problems: the strip packing problem, the two-dimensional bin packing problem, the three-dimensional strip packing problem, and the three-dimensional bin packing problem. For all these problems, we consider orthogonal packings where 90° rotations are allowed. The algorithms we show for these problems have asymptotic performance bounds 1.613, 2.64, 2.76 and 4.89, respectively. We also present an algorithm for the z-oriented three-dimensional packing problem with asymptotic performance bound 2.64. To our knowledge the bounds presented here are the best known for each problem. © Springer-Verlag 2004.2976 359368Baker, B.S., Coffman Jr., E.G., Rivest, R.L., Orthogonal packings in two-dimensions (1980) SIAM Journal on Computing, 9, pp. 846-855Chung, F.R.K., Garey, M.R., Johnson, D.S., On packing two-dimensional bins (1982) SIAM Journal on Algebraic and Discrete Methods, 3, pp. 66-76Coffman Jr., E.G., Garey, M.R., Johnson, D.S., Approximation algorithms for bin packing - An updated survey (1984) Algorithms Design for Computer System Design, pp. 49-106. , G. Ausiello, M. Lucertini, and P. Serafini, editors, Spring-Verlag, New YorkCoffman Jr., E.G., Garey, M.R., Johnson, D.S., (1997) Approximation Algorithms, , ed. D. Hochbaum, chapter Approximation algorithms for bin packing - a survey. PWSCoffman Jr., E.G., Garey, M.R., Johnson, D.S., Tarjan, R.E., Performance bounds for level oriented two-dimensional packing algorithms (1980) SIAM J. on Computing, 9, pp. 808-826De La Fernandez Vega, W., Lueker, G.S., Bin packing can be solved within 1 + ε in linear time (1981) Combinatorica, 1 (4), pp. 349-355Johnson, D.S., (1973) Near-optimal Bin Packing Algorithms, , PhD thesis, Massachusetts Institute of Technology, Cambridge, MassKenyon, C., Remila, E., Approximate strip packing (1996) 37th Annual Symposium on Foundations of Computer Science, pp. 31-36Li, K., Cheng, K.-H., Static job scheduling in partitionable mesh connected systems (1990) Journal of Parallel and Distributed Computing, 10, pp. 152-159Miyazawa, F.K., Wakabayashi, Y., An algorithm for the three-dimensional packing problem with asymptotic performance analysis (1997) Algorithmica, 18 (1), pp. 122-144Miyazawa, F.K., Wakabayashi, Y., Approximation algorithms for the orthogonal z-oriented 3-D packing problem (2000) SIAM Journal on Computing, 29 (3), pp. 1008-1029Vazirani, V.V., (2001) Approximation Algorithms, , Springer-Verlag